北美精算师考试教材5页word文档
北美精算师考试内容及考试制度精算师考试.doc
北美精算师考试制度分为二个阶段：第一阶段是准精算师（ＡＳＡ）。
目前对准精算师的考试要求为300学分。
除了100系列的11门课程（复利数学、精算数学等）外，还须通过200系列的4门课程（经济保障计划、精算实务等）。
每门课在10至30学分不等。
学员在获得300学分后即成为ASA，之后可继续考FSA课程。
ASAl00系列的11门课程的考试均采用英文试卷，选择题形式，考试时间分别为1个半小时至4个小时不等；200系列采用英语书写答题形式。
考生是否通过某一门课程考试以及所获得的分数，是到该课程全部试卷批完后，按成绩顺序排列后确定的。
第二阶段是精算师（ＦＳＡ）。
考生在取得准精算师资格证书后方可参加ＦＳＡ课程考试。
目前把精算师的考试课程分为财务、团体与健康保险、个人人寿与健康保险、养老金、投资五个方向，每个方向又分若干门课，每门课学分在10至30分不等。
要取得ＦＳＡ资格必须通过以上一个方向的所有课程考试，以及再选择以上方向的其他课程，使学分达到150分，即学分总计要达到450分。
当ＦＳＡ要素的课程考试全部通过后，考生还要参加最后一门课程：正式精算师认可课程（ＦＡＣ），其内容主要是职业道德和案例，时间为二天半，一般只要自始至终参加，在结束后的晚宴上会获得ＦＳＡ证书。
北美精算师协会的考点分布在全世界各个国家和地区，考试每年5月和11月举行两次，考试时间由北美精算师协会确定，世界各地统一，考卷由北美精算师协会提供。
报名及考试地点：南开大学、湖南财经学院、复旦大学、中国人民大学、中山大学、中国科技大学、陕西财经学院、平安总公司北美精算学会考试课程准精算师考试：100系列课程：100微积分和线性代数、110概率论和数理统计、120应用统计、130运筹学、135数值分析、140复利数学、150精算数学、151风险理论、160生存模型和生命表编制、161人口数学、165匀修数学200系列课程：200经济保障计划概论、210精算实务概论、220资产管理和公司财务概论、230资产和负债管理原理正精算师的考试课程分为五个方向：一财务包括科目：财务管理、公司财务等二团体和健康保险包括科目：团体和个人健康保险的设计和销售等三个人人寿和年金保险包括科目：个人人寿和年金保险的精算实务调查、人寿保险法和税收等四养老金包括科目：养老金估价原理I、退休计划设计等五投资包括科目：高级资产组合管理等12北美精算师资格考试制度介绍-精算师考试SOA从2005年起采用新的教育体制。
准精算师考试材料word精品文档5页
（一）科目名称：数学基础I1、科目代码：012、考试时间： 3小时3、考试形式：标准化试题4、考试内容：（1）微积分（分数比例：60%）①函数、极限、连续函数的概念及性质反函数复合函数隐函数分段函数基本初等函数的性质初等函数数列极限与函数极限的概念函数的左、右极限无穷小和无穷大的概念及其关系无穷小的比较极限的四则运算函数连续与间断的概念初等函数的连续性闭区间上连续函数的性质②一元函数微积分导数的概念函数可导性与连续性之间的关系导数的四则运算基本初等函数的导数复合函数、反函数和隐函数的导数高阶导数微分的概念和运算法则微分在近似计算中的应用中值定理及其应用洛必达（L’Hospital）法则函数的单调性函数的极值函数图形的凹凸性、拐点及渐近线函数的最大值和最小值原函数与不定积分的概念不定积分的基本性质基本积分公式定积分的概念和基本性质定积分中值定理变上限定积分及导数不定积分和定积分的换元积分法和分部积分法广义积分的概念及计算定积分的应用③多元函数微积分多元函数的概念二元函数的极限与连续性有界闭区间上二元连续函数的性质偏导数的概念与计算多元复合函数及隐函数的求导法高阶偏导数全微分多元函数的极值和条件极值、最大值和最小值二重积分的概念、基本性质和计算无界区域上的简单二重积分的计算曲线的切线方程和法线方程④级数常数项级数收敛与发散的概念级数的基本性质与收敛的必要条件几何级数与p 级数的收敛性正项级数收敛性的判断任意项级数的绝对收敛与条件收敛交错级数莱布尼茨定理幂级数的概念收敛半径和收敛区间幂级数的和函数幂级数在收敛区间内的基本性质简单幂级数的和函数的求法初等函数的幂级数展开式泰勒级数与马克劳林级数⑤常微分方程微分方程的概念可分离变量的微分方程齐次微分方程一阶线性微分方程二阶常系数线性微分方程的求解特解与通解（2）线性代数（分数比例：30%）①行列式n级排列行列式的定义行列式的性质行列式按行（列）展开行列式的计算克莱姆法则②矩阵矩阵的定义及运算矩阵的初等变换初等矩阵矩阵的秩几种特殊矩阵可逆矩阵及矩阵的逆的求法分块矩阵③线性方程组求解线性方程组的消元法 n维向量及向量间的线性关系线性方程组解的结构④向量空间向量空间和向量子空间向量空间的基与维数向量的内积线性变换及正交变换线性变换的核及映像⑤特征值和特征向量矩阵的特征值和特征向量的概念及性质相似矩阵一般矩阵相似于对角阵的条件实对称矩阵的特征值及特征向量若当标准形⑥二次型二次型及其矩阵表示线性替换矩阵的合同化二次型为标准形和规范形正定二次型及正定矩阵（3）运筹学（分数比例：10%）①线性规划线性规划问题的标准形线性规划问题的解的概念单纯形法（包括大M法和两阶段法）单纯形法的矩阵形式对偶理论影子价格对偶单纯形法灵敏度分析②整数规划③动态规划多阶段决策问题动态规划的基本问题和基本方程动态规划的基本定理离散确定性动态规划模型的求解离散随机性动态规划模型的求解5、参考书：①《高等数学讲义》（第二篇数学分析）樊映川编著高等教育出版社②《线性代数》胡显佑四川人民出版社③《运筹学》（修订版） 1990年《运筹学》教材编写组清华大学出版社除以上参考书外，也可参看其他同等水平的参考书。
北美精算学会-SOA-考试制度第2页-精算师考试.doc
财务课程编号名称学分p385财务管理20f580公司财务15f585应用公司财务20f590公司战略和偿付能力管理10团体和健康保险课程编号名称学分g320团体和个人健康保险30的设计和销售g421团体和个人健康保险25的财务管理和法规g422团体和个人健康保险25的定价g522高级品种10g523非养老年金的退休后10和就业前的福利g525灵活的福利计划10g528健康保险专题15个人人寿和年金保险课程编号名称学分l340个人人寿和年金保险30的精算实务调查l343 人寿保险法和税收15n41高级设计和定价25n43估价和财务报告专题25l540个人人寿和年金保险10的营销l545丧失工作能力收入15l550再保险专题15养老金课程编号名称学分p360养老金估价原理15p362退休计划设计15p363养老金筹资工具15p365养老金计划的法律规定25p461养老金估价原理ii和20养老金计划会计标准p560 国际养老金问题20p564作为专家证人的10p567退休收入保障25投资课程编号名称学分v480衍生证券：理论和应用20v485高级资产组合管理15v595资产和负伤管理应用20要取得fsa资格必须通过以上一个方向的所有课程考试，以及再选择以上方向的其他课程，使学分达到150分，即学分总计要达到450分。
此外，当fsa要素的课程考试全部通过后，考生还要参加最后一门课程一一正认可课程(fac)，其内容主要是职业道德和案例，时间为二天半，一般只要自始自终参加，在结束后的晚宴上会获得fsa证书。
到1996年，北美精算学会共有会员16，558名，其中美国11，961名，加拿大3，161名，其他国家1，436名，(除了fsa、asa外，还包括少量的财产和意外险和美国养老金)20，592人，其中美国15，695人，加拿大3，355人，其他国家1，542人。
北美精算学会的考点分布在全世界28个国家和地区，考试每年在春季(五月)和秋季(十一月)举行两次，全世界每年有数干人参加asa一万多门次课程的考试，其中asa的平均通过率为40％。
【资格考试】北美精算学会考试课程
正精算师的考试课程分为五个方向：
一财务包括科目：财务管理、公司财务等
二团体和健康保险包括科目：团体和个人健康保险的设计和销售等
三个人人寿和年金保险包括科目：个人人寿和年金保险的精算实务调查、人寿保险法和税收等
【资格考试】北美精算学会考试课程
编 辑：__________________
时 间：__________________
北美精算学会考试课程
准精算师考试：
100系列课程：100微积分和线性代数、110概率论和数理统计、120应用统计、130运筹学、135数值分析、140复利数学、150精算数学、151风险理论、160生存模型和生命表编制、161人口数学、16投资包括科目：高级资产组合管理等
PAKStudyManualQF-北美精算师（QFIQF）
PAKStudyManualQF-北美精算师（QFIQF）Intro-Maths-Fin-1Financial Derivatives (A Brief Introduction )Background This chapter deals with the two basic building blocks of financial derivatives:1. Options2. Forwards and futures.We briefly introduce the third class of derivative: swap. We see how a complex swap can be decomposed into a number of forwards and options.Definitions Derivatives securities are financial contracts that ‘derive’ their value from cash market instruments such as stocks, bonds, currencies and commodities.At the time of the maturity of the derivative contract, denoted by T , the price F(T) of the derivative asset is completely determined by the market price of the underlying asset (S T ).For instance, the value at maturity (T ) of a long position in a call option of strike (K) written on an asset (S T ) is:Max [S T ?K ;0]Also, the value of time T of a long position in a forward contract of forward price (F) written on an underlying asset worth (S(T) at time T is given by:S (T )?FTypes of derivatives We group derivatives into three general headings:1. Futures, Forwards, Repos, Reverse Repos and Flexible Repos (Basic building blocks )2. Options and3. SwapsMany of these instruments will be discussed in other parts of the syllabus for the QF Exam.The underlying asset: We let (S t ) represent the price of the relevant cash instrument, which we call the underlying asset . The five main groups of underlying asset : We list five main groups of underlying assets:1.Stocks (These are claims on “real” returns)2.Currencies3.Interest rates: Interest rate in not an asset, so we are referring to the direction of interest rates. The assets are Treasuries, bonds.4.Indexes (S&P 500) and/doc/186969871837f111f18583d049649b6648d70912.html modities: they are not financial assets either, they are goods in kind. There is another method for classifying the underlying asset:1.The cash and carry markets and2.The price discovery marketsLet us discuss these two marketsThis new classification is important to us.In the cash and carry market, one can borrow at risk-free rates, buy and store the product,and insure it until the expiration date of any derivative contract.Pure cash and carry market have one property: Information about demand and suppliesof the underlying instrument should not influence the spread between cash andfutures (forward) prices.In the Pure cash and carry market, any relevant information concerning future supplies anddemands of the underlying instrument is expected to make the cash price and the future price change by the same amount (This is not so, in the price discovery market).In the price discovery market, it is physically impossible to buy the underlying instrumentfor cash and store it until some future expiration date. That strategy (of borrowing, buying and storing) is no longer applicable. In the price discovery market, any information about the future supply and demand of theunderlying commodity cannot influence the corresponding cash price.Expiration DateAt the expiration of the forward/futures contract, we expect:At expiration,t?e Futures price=F(T)=T?e spot price of t?e underlying asset=S T But, during the life of the futures contract (t Forward1 and FuturesForwards and Futures are linear instruments (while options are nonlinear instruments).“Options are non-linear instruments because the derivative of the payoff function changes sign around the strike price. In fact, the payoff of an option is a convex function of the underlying asset”Definition of a forward contractA long forward contract is an obligation to buy an underlying asset at a specified forward price (or the strike price F) on a known date (the maturity T). The contract requires no initial premium (it costs nothing to enter into the contract). At expiration, the holder of the forward contract (the long position) purchases the asset at the forward price (agreed upon at contract inception)2.The long position in a forward contract makes money when the price at expiration of the underlying asset exceeds the agreed-upon forward price. Thus:Payoff of long forward position=S(T)?F Where:S(T)=T?e spot price of t?e underlying asset at t?e expiration of t?e contract(T) F=T?e forward price (agreed upon at contract inception)The short position profits only when prices fall, and thus:Payoff of s?ort forward position=F?S(T)=?Payoff of long position Graphically:1 In Chapter 5 of Fixed Income Securities (FIS-5), we discuss forward contracts as they apply to fixed income instruments: The underlying asset will be (i) a ZCB and then (ii) a coupon-paying bond. 2From a risk management perspective, the long position (buyer of the forward contract) isThe short position in the forward contract is graphically represented below3:Note the following points:Though the initial value of the forward contract is zero, the contract surely has valueduring its life. At any time (t) less than maturity (T), the contract is worth (S t?PV t(F)),where (PV t(F)) is the present value of the forward price calculated at time (t) and (S t)is the underlying asset spot price as of time t.4If at expiration (T), the spot price of the underlying asset matches the agreed uponfuture price (F), then there is no profit to be made under the forward contract.The forward contract is a zero-sum game in a sense that the gain to one party is the lossto the other party.The short position in the forward contract is the party who wrote the contract and soldto the long position. The short position has an obligation/liability at maturity towards3 The payoff clearly exhibits an unlimited loss when the underlying asset price (S T) exceeds the forward price (F).the long position only if (S(T)>F). However, if (S(T)diagram, the short position in the forward contract will benefit from the contract.The slope of the line is 1, and the forward contract is referred to as a ‘linear contract’.Futures and forwards are similar instruments. The major differences between them can be stated briefly as follows:1.Futures are traded in organized exchanges and forwards are custom-made and traded over the counter.2.Futures exchanges are cleared through exchanges clearing houses and there is a mechanism designed to reduce default risk. Forwards are not cleared and there is default risk.3.Futures contracts are market to market. Every day, the contract is settled and a new contract is entered.4.The security underlying the futures contract is standardized (the type of security is clearly specified and the timing and method of delivery as well). Forward contracts can be customized.5.Because of the mark-to-market system in the futures contracts, they have less credit risk than forward contracts (same point as point 2).Repos, Reverse Repos, and Flexible Repos5In a Repo (Repurchase agreement), one party sells securities to another party in returnfor cash, with an agreement to repurchase the securities (or equivalent) at a pre-agreed price (the repurchase price) and pre-agreed time (the maturity date).The long position in a repo (the buyer) acts as a lender of cash, and the short position (theseller) as a borrower.For the party selling the security and agreeing to repurchase it in the future, the transactionis a repo. For the party on the other end, the transaction is a reverse repo.The securities are used as collateral in this transaction.Profit from a repoAssume that a trader is entering into a repo transaction with a Repo Dealer as follows:P t=T?e price of t?e collateral asset at time t5At time t, the trader exchanges this underlying asset in return for cash received from the Repo Dealer. The Repo Dealer pays (P t )6Amount borrowed from t?e Repo Dealer =P t.At maturity of the repo (time T ), the trader must repurchase the underlying asset from the Repo Dealer. This underlying asset worth is now worth (P T ). But under the repo transaction, both parties would have agreed upon a repurchase price (reflecting the interest earned on the repo transaction). Let:X T =T?e agreed upon repurc?ase price of t?e collateralWe have:X T =P t ×[1+Repo rate ]At time T, the trader repurchases the security at price (X T ) and sells it back in the market for (P T ).Uses of repos Repos are used to raise short term capital and are classified as money market instruments as a consequence.Categories of repos There are three broad categories of repos:1) Overnight repos: A one day maturity repo transaction. 2) Term repos: This is a repo with a specified maturity. 3) Open repo: This repo has no end date.A flexible repo is a repo with a flexible withdrawal schedule. Therefore, the party holding the collateral can sell it in parts before or at the maturity of the repo. There are two types of flexible repos:1) Secured : The municipality/customer receives collateral in the form of Treasury bonds,GNMA bonds, agency MBS/CMO.2) Unsecured : The customer does not receive collateral. The deal commands a higher spread.Differences between flexible repos and traditional repos: They are four major differences with a traditional repo:1) Convexity due to cash withdrawals, 2) Formal written auction like trade, 3) Enhanced documentation,4) Counterparties are usually municipal bond issuers.Options6Forwards and futures obligate the holder to deliver or accept the delivery of the underlyinginstrument at expiration. Options, on the other hand give the owner the right (not the obligation) to purchase or sell an asset.Call option Consider an investor who purchases a call option written on an underlying asset 7As such, the payoff of the long call option (the call option buyer) is: . The initial spot price of the asset is (S 0). The investor pays a premium (c ) to be able to take advantage of theflexibility offered in the option contract. The option matures at time (T ), when the underlying asset has a spot price of (S T ). The future spot price is unknown to all market participants when entering into the option initially (t=0). The option gives the investor the right (but not the obligation) to purchase the asset at time T , for a pre-agreed price of K (or X, or Strike), called the strike price.Long call option maturity payoff =?S TK if S T >K 0 if S T ≤KTo put words into the mathematics, we say this:If at maturity of the option (T ), the underlying asset (S T ) is worth less than the strike (K ), the option buyer will not exercise his/her option. The instrument ends worthless.If at maturity of the option (T ), the underlying asset (S T ) is worth moreLong call option maturity payoff =Max (S T ?K ;0)than the strike (K ), the option buyer will exercise his/her option, and the payoff is the excess of the asset’s value over the strike (S T ?K ). Thus, we also write:The payoff of the short position (the call option writer) is the opposite of the long position as follows:Short call option maturity payoff =?(S T K ) if S T >K 0 if S T ≤KThe premium (c)8Profit for t?e long position =(Maturity Payoff of t?e long position )?FV (Premium ) must be adjusted from the payoff in order to get the net profit for each position: AndProfit for t?e s?ort position =(Maturity Payoff of t?e short position )+FV (Premium ) Or:Profit for t?e s?ort position =FV (Premium )?(Maturity Payoff of t?e long position )7 We assume that the underlying asset pays no dividends during the life of the option.8 This premium represents the compensation the seller accepts for the right granted to the buyer.option .Graphically:Put option Consider an investor who purchases a put option written on an underlying asset. The initial spot price of the asset is (S 0) at contract inception. The investor pays a premium (p) for the put option. The option matures at time (T ), when the underlying asset has a spot price (S T ). The future spot price (S T ) is unknown to both parties at the inception of the put contract. At maturity of thecontract, the long position will decide on whether to exercise his/her option to sell the asset for the strike price (K ):If at maturity of the option (T ), the underlying asset (S T ) is worth less than the strike (K ), the put option buyer (the long position in the put option) has the ability to sell at price (K ), an asset that is worth less than (K ). He/she will exercise his/her option. The payoff from exercising this option is clearly equaled to (K ?S T ).If at maturity of the option (T ), the underlying asset (S T ) is worth more than the strike (K ), the put option buyer (the long position in the put option) has the ability to sell at price (K ), an asset that is worth moreLong put option maturity payoff =? K ?S T if S Tthan (K ). He/she will not exercise his/her option. Thus, the instrument ends worthless. Thus, the maturity payoff of the long put option is:Or also:Max (K ?S T ;0)The payoff of the short position (the option writer) is the mirror image as follows:Short put option maturity payoff =?(K S T ) if S TNote : From the perspective of the buyer, it is interesting to buy the put option when you think that the underlying asset ‘might’decrease below the strike price. You can also purchase the put option ifoption + asset) is comparable to owning an insurance contract9 on an asset (subject to damage in value).Graphically the payoff/profit of a call option (long/short) are plotted below: Also, the payoff/profit of a put option (long/short) are plotted below:Let us consider other reasons why would a trader may consider buying options:Reasons why traders may want to calculate the arbitrage-free price of a call option1.New contract: before the option is first issued, a trader may want to know the price that the option will trade at.2.Mispricing: A trader may want to calculate the arbitrage free value of an option to determine if the option is mispriced in the market.9 In fact, in the financial economics literature, the portfolio containing the stock and the put option written on the stock is called a protective put. Likewise, the writer (seller) of the call might want to protect himself from a huge increase in the stock index, as such, he/she would buy the underlying7.1).The profit at maturity (T ) of the derivative to the longProfit (Long position )=Payoff of the Long Position (T )?FV (Premium )position is calculated as: WhereFV (Premium )=T?e Future Value of t?e Premium paid at inception by t?e long positionAlso, the profit at maturity (T ) of the derivative to the shortProfit (Short position )=FV (Premium )?Liability of the Short Position (T )position is calculated as:WhereLiability of t?e S?ort Position (T )=Payoff of t?e Long Position (T )We build the cash flows table as follows:As already explained:The long position in a stock is purchasing the stock price today (a negative cash flow) to receive the proceeds from the sale of the stock at maturity (a positive cash flow).The short position in a stock receives money from selling the stock today (a positive cash flow) and has to redeem the stock at maturity (negative cash flow). The long stock and the short stock are in a zero-sum game.The long position in a ZCB of redemption value K has to pay for the ZCB today. The price of which is the PV of the redemption amount. Because this is a purchase, it is a negative cash flow. At maturity though, the long position receives the redemption value of the bond K, a positive cash flow.The long position in any derivative has to pay a premium for entering into the derivative transaction at time t=0 (negative cash flow). At maturity, this long position is entitled to a payoff.The short position in any derivative receives the premium from the long position (positive cash flow) and at maturity; the short position is responsible for paying off the payoff arising to the long position. Because this payoff is a liability, it is a negative cash flow.10 Though not directly discussed in Neftci-1, the concept here is discussed in FIS-6 and frankly theA swap is an agreement between two counterparties for selling and purchasing cash flowsinvolving various currencies, interest rates and a number of other financial assets.The counterparties borrow in sectors where they have an advantage and then exchange theinterest payments.In a simple IRS, at the end, both counterparties secure a lower rates and the swap dealerwill earn a fee.The simple IRS exampleThis contract allows parties to exchange payments between two differently indexed legs, starting from a future time instant (Tα). At every time (T i), the fixed leg pays out the amount:Notional×τi×KWhere: τi=T?e year fraction between T i?1and T iK=T?e fixed rate of interest for t?e fixed payments of t?e IRS swapNotional=T?e notional amount of t?e swap Whereas the floating leg pays out the amount:Notional×τi×L(T i?1,T i)Where: L(T i?1,T i)=T?e floating rate t?at resets at t?e previous time (T i?1) and is used t?e payment at time (T i) Graphically, we have:A counter-party in this plan vanilla swap may be able to close out the transaction by payingthe net present value (NPV) of future swap payments.Pricing swaps11One method for pricing swaps and swaptions is to decompose them into forwards andoptions.The forwards can then be priced separately, and the corresponding value of the swap can bedetermined from these numbers.Two examples of swaps1)The simple IRS (Interest Rate Swap): Each counter-party borrows in the market (fixed rate and floating rate market) where it has an advantage and they both exchange the payments.2)The Cancelable Swaps: In this swap, each party has the option to cancel the transaction before maturity and extinguish the obligation to pay the PV of future payments. They come in two flavors: Callable swaps and Puttable swaps.Some properties of Cancelable swapsPopular among institutions with an obligation in which they are to repay principal beforematurity. The embedded option on the swap can be exercised to honor such liabilities.They can be used as hedge instruments.They allow institutions to mitigate maturity mismatch between assets and liabilities due toprepayments options or early surrenders.Past examsSOA Spring 2015 QFIC Q11 on Repo (Must Read)SOA Spring 2013 APM Q3 (Must Read)PAK Practice questionsQuestion 1a)List the differences between forwards and futures:Question 2Assume that the S&P 500 index is at 100. For a single premium of $100, a life insurance company had sold the following type of products:Contract 1: promising to pay 100 at maturity of the contract in 5 years plus any excess of the S&P 500 over its initial value of 100.Contract 2: The Company promises to pay the excess of two quantities:90% of the initial premium accumulated at 2% per annum andThe proceeds from the investment of the initial premium into a fund that performs exactlyFor each contract, determine the following quantities:1.The maturity of the contract2.The type of derivative embedded in the liability and the underlying asset.3.Identify the payoff of the liability, and the strike amountQuestion 3a)Describe the bull call spread optionQuestion 4a)Show the payoff of a cap portfolio (short stock + long call): In mathematical terms andthe plot.b)What is the net profit of the cap portfolio?c)Show that the ca portfolio can be viewed as a long put position.SolutionQuestion 1: Differences between futures and forward contractsThere are important differences between these two contracts:Forward contracts are settled at expiration while futures contracts are settled daily. At the end of each trading day, the clearinghouse adjusts the margin accounts to reflect the daily gain/loss to each counterparty of the transaction. This is called mark-to-market.Forward contracts are settled at the agreed-upon forward price while futures contracts aresettled at the settlement price determined on the last trading date.In a forward contract, there are no cash flows until expiration whereas for a futurescontract, there are daily cash flows to reflect the gain and loss to each counterparty.Futures contracts are more liquid than forward contracts. Futures contracts can be offsetany day by entering into an opposite transaction.Because of the daily mark-to-market accounting, futures contracts have lower (if any) creditrisk than forward contracts.There are typically daily price limits in future markets. Such limits are market moves thattrigger a temporary halt in trading.Question 2: Life insurance index contract1.Contract 1 has a maturity of 5 years and contract 2 has a maturity of 10 years.2 and 3.Embedded derivative in Contract 1:A call option on the S&P 500 of maturity 5 and strike 100.Embedded derivative in contract 2:Payoff is:Max (0.9×100×(1.02)10;F 10)Where:F 10=t?e terminal value of t?e fund t?at mimics t?e S &P 500The payoff is equal to:Max (109.7;F 10)=F 10+Max (0;109.7?F 10)=F 10+Payoff of a put optionThus, the embedded derivative is a put option on the underlying fund of strike 109.7 and maturity 10 years .Question 3: The Bull spread 12Bull Call Spread Option (Neftci practice problem 6 on page 11)A bull spread call is a strategy that involves purchasing call options at a specific strike pricewhile also selling the same number of calls of the same asset and expiration date but at a higher strike.A bull call spread is used when a moderate rise in the price of the underlying asset is expected.The maximum profit in this strategy is the difference between the strike prices of the long and short options, less the net cost of options.Question 4: The cap portfolioThe combination (short asset and long call option on the asset) is called a cap 13. Let us now look at the mathematics of the cap (c-S ). The payoff table is captured below:Note the following about the payoff of the cap position:Max (0; S (T )?K )?S (T )=?If S (T )?K ) T?e payoff is –S (T ) If S (T )>K or if (–S (T )12 More of this type of strategies in QFIQ-120-19 section 4.13The insight here is that without the call option, the short position in the asset has anobligation/liability of amount (S(T)) at maturity time T . However, with the long call option added to exceed that strike level . Note:That is why in the table, the final payoff for the position is simply (Max(?S(T);?K)).It is also very important to realize that the expression (Max(?S(T);?K)) is not the same as(?Max(S(T);K))14.Graphically, the maturity payoff of (the sum of the short stock + the long call option) yields a liability (opposite payoff) that cannot exceed a certain cap (the opposite of the strike level) as can be depicted below:Where we clearly see that when (S(T)K), the liability (opposite payoff) of the cap is (?K).The net profit of the capAs explained earlier on also, the profit at maturity (T) of the derivative to the short position is always calculated as:Profit(Short position)=FV(Premium)+Liability of the Short Position(T) Where Liability of t?e S?ort Position(T)=?Payoff of t?e Long Position(T) Thus, the net profit from the cap is calculated as:Max??K;?S(T)?+FV[S(0)?c]Thus:14For instance, (Max(?3;?10)=?3) while (?Max(3;10)=?10). These are two differentProfit from the cap portfolio=Max??K;?S(T)?+[S(0)?c]×(1+r)TThe cap can be viewed as a long putWe are claiming that the net profit of the cap is equal to the net profit of a long put. How so? Once again, we make use of the put call parity identity:c?S(0)=p?K×(1+r)?T Multiplying this line by the accumulation factor (?(1+r)T), we get:[S(0)?c]×(1+r)T=?p×(1+r)T+KBy substitution of the FV of the premium ([S(0)?c](1+r)T) into the net profit for the cap, we get: Profit from the capportfolio=Max??K,?S(T)??p×(1+r)T+KBy allowing K to enter into the Max-term, we get:Profit from the cap portfolio=Max?K?K;K?S(T)??p×(1+r)T Thus: Profit from the cap portfolio=Max?0;K?S(T)??p×(1+r)T=Profit for a long put option。
北美精算师考试
想考北美壽險精算師的朋友們請看過來！撰文＆資料整理：ducklmh 05/26/2007首先：報考SOA 考試沒有任何身分限制↓這些是基本的預備知識Calculus （微積分）Linear Algebra （線性代數）Introductory Accounting （初級會計學） Elements of Business Law （商事法基礎） Prerequisite （預備知識）Mathematical Statistics （數理統計學）備註為應考人應擁有之預備知識，SOA 不做任何考試驗證其能力。
↓請您把握在學期間把以下課程修一修吧！Microeconomics （個體經濟學） Economics （經濟學）Macroeconomics （總體經濟學） Finance （財務管理） Corporate Finance （公司財務） Investment （投資學） Regression （迴歸分析）Validation by EducationalExperience（修習學分認可，簡稱VEE ） Applied Statistical Methods（應用統計方法）Time Series （時間序列分析）備註一 VEE 分為以上此三科目 每科目又涵蓋各兩部份備註二1. VEE 為SOA 所設計之新制度，把以往這些考試內容，改由應考人自己在大學或研究所修習過之這些科目學分，經由SOA 認可後即可獲得VEE 學分，或可參加SOA 之網路線上教學取得該三科目之學分。
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北美精算师介绍课程的介绍精算师考试.doc
ASA的课程课程1：精算科学的数学基础(MathematicalfoundationsofActuarialScience)这门课程的目的是为了培养关于一些基础数学工具的知识，形成从数量角度评估风险的能力，特别是应用这些工具来解决精算科学中的问题。
主要内容及概念：微积分、概率论、风险管理（包括损失频率、损失金额、自留额、免赔额、共同保险和风险保费）。
课程2：利息理论，经济与金融(InterestTheory，EconomicsandFinance)这门课程包括利息理论，中级微观经济学和宏观经济学，金融学基础。
课程3：关于风险的精算模型(ActuaricalModels)通过这门课程的学习，培养学员关于随机事件的精算模型的基础知识及这些模型在保险和金融风险中的应用。
主要内容包括：保险和其它金融随机事件，生存模型，人口数据分析，定量分析随机事件的金融影响。
课程4：精算建模方法（ActuarialModeling）该课程初步介绍了建立模型的基础知识和用于建模的重要的精算和统计方法。
主要内容包括：为何及如何选择和使用模型，回归分析，风险理论和信用理论。
课程5：基本精算原理的应用(ApplicationofBasicActuarialPrinciples)这门课程提供了产品设计，风险分类，定价/费率拟定/建立保险基金，营销，分配，管理和估价的学习。
覆盖的范围包括金融保障计划,职工福利计划，事故抚恤计划，政府社会保险和养老计划及一些新兴的应用领域如产品责任，担保的评估，环境的维护成本和制造业的应用。
课程6：金融与投资(FinanceandInvestments)该课程是用于投资和资产负债管理领域的精算原理的拓展。
学员在完成该课程的学习后，将会对资本市场、投资工具、衍生证券及应用、投资组合管理和资产－负债管理有深入的了解。
主要内容及概念：资本市场和基本投资原理，投资工具，衍生证券，投资组合管理的原理，资产负债管理。
Bhbeeon精算师非寿险精算数学
Time will pierce the surface or youth, will be on the beauty of the ditch dug a shallow groove ; Jane will eat rare!A born beauty, anything to escape his sickle sweep
.-- Shakespeare 非寿险精算数学(05)考试大纲
考试时间：3小时
考试形式：书面、闭卷
试题类型：客观判断题
考试内容和要求：
一．损失分布（15%）
1．基础风险资本（RBC）
2．损失分布的数字特征
3．损失额分布
4．损失次数分布
二．总损失的数学模型（10%）
1．独立随机变量和的分布
2．总损失额的分布（个别风险模型）
3．总损失额的分布（聚合风险模型）
三．损失分布的统计推断（15%）1．损失分布的拟合和拟合优度检验2．贝叶斯方法
3．信度理论基础
四．损失分布的随机模拟（15%）1．损失额的随机模拟
2．损失次数的随机模拟
3．总损失额的随机模拟
4．随机模拟的次数和精度
五．相关分析和回归分析（10%）1．相关分析
2．线性回归分析
3．非线性回归分析
六．时间序列分析（15%）
1．时间序列及其指标分析
2．时间序列的外推模型
3．随机型时间序列分析
七．效用理论（10%）1．效用期望决策
2．非寿险定价
八．随机过程（10%）1．泊松过程
2．马尔可夫链
3．破产概率
4．无赔款优待折扣（NCD）。
【北美精算师考试】lossmodels
Errata and clarifications for Loss Models: From Data to DecisionsPage 32, at the end of the line prior to the formula at the bottom of the page, add the footnote: The tilde on the indicates that this is an approximation due to grouping.I Page 44, line 6: Replace "valuet" with "value"Page 67, Theorem 2.3: The coveriance matrix in the third to last line of the statement of the Theorem must be divided by to read .n Ð`ÑÐ`ÑÎ8g g w D Page 68, Example 2.27: Only the first factor in the third term on line 2 of the string of equations has a zero expectation. This is sufficient for that term to be zero. The secondterm is only approximately zero because is only asymptotically unbiased./.5s s Î##Page 74, Corollary 2.6: Change part of it to read "The expected payment, per payment,provided 1, is"J Ò.ÎÐ" <ÑÓ Page 75, Definition 2.28: In the last line, replace "" with "";and exist exists IÐ\•.Ñand in the second to last paragraph: In the first line, replace "moments" with "firstmoment"; in the third line replace "could be either" with "is"; in the fourth and fifth lines,delete "or because does not converge. If the second limit exists,lim .Ä!.'B0ÐBÑ.B IÐ\•BÑ will still exist."; and in the seventh, eighth, and ninth lines, delete "If the first limit exists but the second does not, both and will fail to exist, but the IÐ\ÑIÐ\•BÑdifference will."Page 76, Definition 2.29: After "it is" add ", provided 1,"J Ð.Ñ \Page 76, line 5: Replace "due to having a heavy tail," with "(for example, if the \distribution is heavy-tailed)"Page 94, Definition 2.34: It should be noted that must be positive.!Page 137, second line of Example 2.74: Replace "This data are" with "This data set is"Page 165, Exercise 2.44: The last sentence should be: "Keep the two samples separate so that (2.14) can be used. Then construct a 95% confidence interval for the mean."Page 168, line 1 of Exercise 2.67: Replace "gamma" with "inverse Weibull"Page 190, Table 2.38: The fifth row of the table should be 4–13 and not 5–13.Page 199, Introduction: It should be made clear that throughout Chapter 3 all random variables have the non-negative integers as the set of possible values.Page 205, near the bottom: It should be noted that .8œ8D 5œ!_5Page 206, last line: Replace "numbers of claims per day" with "number of days with a given number of claims"Page 210, Definition 3.2: It should be noted that the definition that uses the gamma function applies only if 1.B 5 Page 241, last line: Replace "" with ""T ÐDÑT ÐDÑX X #Page 257, In Definition 3.6, it should be noted that refers to the square root of .3 "Page 258, In the last line of Equation (3.38), the exponent in the expectation should be an uppercase theta () rather than lower case.@Page 264, first paragraph after the end of Exmaple 3.33: Note that while the binomial distribution is not infinitely divisible,if is an integer, then the binomial 78Î8‡distribution is preserved.Page 265, just before Example 3.35: Note that the "number of data points" is the number of years, not the number of exposures.Page 267, ZM Poisson entry in Tble 3.21: The greek (nu) in the third term in the /numerator should be the letter (vee).@Page 271, Exercise 3.5: The information referred to is in the table at the top of the page.Page 279, Exercise 3.34: Add a condition of independence. That is, let have W 3independent compound Poisson frequency distributions...Page 296, At the end of equation (4.4) add for Also, on the following line 5œ"ß#ßáÞchange the text to "with probability zero on negative values." Finally, the equation after (4.4) holds only for For , this equation reduces to .5œ#ß$ßáÞ5œ"0ÐBÑœ0ÐBÑ\‡"\The same holds for the equation at the top of page 297. At the bottom of page 296,change "with probabilities at" to "with positive probabilities only at"Page 308, in the footnote, change the expression on the second to last line toT <Ð\œC Ñ !3.Page 316, add the following after line 6: "A reason to favor matching zero or onemoment is that the resulting probabilities will always be non-negative. When matching two or more moments, this cannot be guaranteed."Page 358, Exercise 4.5: Change the standard deviation of "Room" from 300 to 500.Page 361, Exercise 4.18: In the second table, the entries under should be 1 and 10, notB0 and 10.Page 363, Exercise 4.24: There should not be an exercise number here. This paragraph is the conclusion to Exercise 4.23. To match the answers in the solutions manual, all subsequent exercises in this chapter should be numbered one less.policyholder,where n is the Page 413, Example 5.19: In the second line, after "" insert "number of exposure units,"Page 417, First paragraph of solution to Example 5.23: Replace from the sentence0œQœbeginning "Now 175" to the end of the solution with "Now 175 and we assume8œœthat will be 140 for this group. Thus, with 210 and 1,082.41 we use (5.38) 5-!0\œwith estimated by 150 to obtainÈ1501402101,082.410.472^œÐÎÑÎœ\(note that is the average of 210 claims, so approximate normality is assumed by the central limit theorem). Thus the net premium per life insured is0.4721500.528175163.2.TœÐÑÐÑ ÐÑÐÑœ-The net premium for the whole group is 125163.220,400.ÐÑœÐÑœÐÑœPage 449, after (5.68): The assumption must be changed to 0.1)1)!"Page 461, line three of third paragraph: Replace "by" with "be"Page 468, paragraph before Example 5.47: It reads better if the second and third to last sentences are switched.Page 488, Exercise 5.44: Add "expected" before "number of claims" in the second to last line., Exercise 5.47(c) and , Exercise 5.48(c): In both cases add "for each Page 489page 490)" at the end.Page 491, Exercise 5.50: In line 5 change "mean" to "means" and "variance" to "variances"1)1)ÐÑœÐÑœPage 493, Exercise 5.56(f): Change the requirement to 0.!"Page 493, Exercise 5.57(b): Change the left hand side to IÐ\l\ â \œ=Ñ8 ""8Page 495, Exercise 5.67: On the second line change the decimals to the exact fractions 1/6 and 5/36 and on the fourth line change the decimals to the exact fractions 5/6 and5/36.Page 496, Exercise 5.68: Change the Bühlmann numbers to 2.72, 7.71, and 10.57.Page 496, Exercise 5.67(b): Place a 0 before the decimal point in .25.Page 497, Exercise 5.73: There is an extra | in a subscript in the second bullet.page 499, Exercise 5.79: In the third-fifth bullets, and should be upper case to .-indicate that they are random variables.Page 510, first number in the column headed by "4": Change "1 ,441" to "1,441"Page 609, last line: Add an "" after ""2Ð4 "Î#ÑPage 610, last line: Add an "" after ""2Ð4 "Î#ÑPage 614, line 4 of section H.4: Replace "" with ""X +X +88Page 620, answer to Exercise 3.19(a), change the answer toFor 1,2,3,4,5,6,7the values are 0.276, 2.315, 2.432, 2.891, 4.394, 2.828, and 4.268,5œwhich, if anything, are increasing. The negative binomial or geometric model may work well.Page 622, answer to Exercise 4.19, the difference is 14.78.Page 626, answer to Exercise 5.68 should be expressed as 1210.6.IÐ\l\œÑœ#"Errata for the Solutions Manual to Loss Models: From Data to DecisionsExercise 2.3, page 2: The expression in parentheses in the equation for should be <Ð. -. -Ñ##.Exercise 2.6, page 3: The denominator should be 96,000 and not 60,000. The answer is correct.Exercise 2.39, page 10: All of the ratios of with a subscript over should be have the -)) in the numerator and the subscripted in the denominator. The answer is correct.-Exercise 2.45, page 14: The information matrix isMÐßÑœs s !"”•1.707900.01668610.01668610.000176536.Exercise2.67, page 20: Change the solution to read as follows:The parameter estimates are 0.963933 and 94.3501.7)s œœs IÐ\•ÑœÒ" Ð ÑÓ10,00094.35010.0374165; 0.011163> Ò" /B:Ð ÑÓœ10,0000.011163516.09.Similarly, 5,000440.28 and the answer is .8516.09440.2860.648.IÐ\•ÑœÐ ÑœThe per payment expected value is60.648500060.6480.021542,815.60.ÎÒ" J ÐÑӜΜExercise 2.115(b), page 37: In the expression 3510 in the final ratio, replace the exp Ð ÎÑ10 with 20. The answer is correct.Exercise 2.118, page 37: In the last line, change the "" to a comma.Q Exercise 3.6(c), page 44: The test statistic is 0.23 2.73 2.60 5.56.œExercise 3.10, page 48: The solution is 0.471494 and 0.352072.!)"œ<œœœExercise 3.12, page 48: Both (b) parts have the confidence interval missing. The first one is 0.1001 1.960.000011012 or 0.10010.0065 and the second one is …ÐÑ…"Î#0.166 1.960.000193556 or 0.1660.027.…ÐÑ…"Î#Exercise 3.19(a), page 53: Replace the solution with the following:For 1,2,3,4,5,6,7the values are 0.276, 2.315, 2.432, 2.891, 4.394, 2.828, and 4.268,5œwhich, if anything, are increasing. The negative binomial or geometric model may work well.Exercise 3.47, page 68: Replace the last sentence with the following:Because the variance is , the goodness-of-fit test statistic equals the Poisson /Ð" Ñ5""test statistic divided by or 6.191.09772 5.64. The geometric model is accepted." Îœ"Exercise 3.49, page 68: The first paragraph of the correct solution is:@œÒ" J ÐÑÓÎÒ" J ÐÑÓœÎÞ1000500916 The original frequency distribution is P-ETNB with 3, 0.5, and 2. The new frequency distribution is P-ZMNB-"œ<œ œwith 3, 0.5, 291698, and 0.37472.-"œ<œ œÐÎÑœÎ:œœQ !!œ$ Ð"(Î)Ñ !Ð"(Î)Ñ" $Þ&Þ&Þ&Þ&This is equivalent to a P-ETNB distribution with 310.37472 1.87584,-œÐ Ñœ<œ œÎœœÎ0.5, and 98, which is P-IG with 1.87584 and 98."-"In the first line of the second paragraph, replace the equals sign in the numerator with a minus sign.Exercise 4.14, page 75: All of the + signs should be subscripts, not superscripts. The letter should be used in place of for the random variable.\W Exercise 4.16, page 76: 505025 and the solution is 2/3.IÐEÑœ5 55œ "Exercise 4.19, page 77: The second line for the variance should be1061265,000. The premium is 100514.18 for a difference of 14.78.7;Ð ;Ñœ7; #Exercise 4.22, page 77: The third term in the sum should be 0.1Pr .Š‹^ 10030027 ÈExercise 4.24 and beyond in chapter 4: In the text the problem numbers are one higher than the number given here.Exercise 4.25, page 79: The final equation is0.9Pr 1.53431 1.534. The answer isœÒW Ÿ ÎÓœB .B œ Ò ÎÓ--ÈÈ'""Þ& $Î% %-Ècorrect.Exercise 4.62, page 90: The solution is correct, but the notation is misleading. ChangeJ ÐBÑJ ÐBÑ8J ‡8W 8W ‡Ð8 "Ñ to to reflect the distribution using all policies and change toJ 8 "8 " to reflect the distribution using only the first policies.Exercise 5.22, page 106: In answer (c) the integral is 13, which is 0.35. Therefore,Î only (a) is possible.Exercise 5.38, page 111: In Table 4.4, the first entry in the column headed "2" should be 0.0625.Exercise 5.38, page 112: In part (h) the last four probabilities should have the events separated by commas and not by bars. Also, two of the probabilities need to be changed:Pr 0.118329 and Pr 3 0.046367. In part (i), the Ð\œ#ß\œ#ÑœÐ\œß\œ#Ñœ#"#"probability to divide by is 0.343333.Exercise 5.50, page 114: 0.050.125,0000.11001,400.+œÒ ÐÑÓÐÑ ÐÑÐÑœ=###5œÎœ^œÎÐ Ñœ5,0001,400 3.5714, 33 3.57140.4565,T œÐÎÑ ÐÑœ-0.456520030.54351035.87.Exercise 5.56(d), page 119: Add horizontal space between (d) and (e).Exercise 5.58(b), page 122: Need a minus sign inZ ÐÑœÐ Ñ Ðœ2123456 3.5) 2.917.#######Exercise 5.59(b), page 122: Because the support of the prior distribution is 1, that is ) also the support of the posterior distribution. Therefore, it is not a gamma distribution.The constant to make it a density is'’“"_ #"' # #""'"'x #%)#"'Ð"&Ñ/.œ/ â œ/)))"(1,179,501,863. The posteriormean is then '’“"_ #" #"""x #%)#"Ð"Ñ/.Î/œ âÎ)))777761,179,501,8631,179,501,863 which"8is 10,025,765,8381,179,501,8638.5. (Actually, the ratio is slightly less than 8.5.)ÎœExercise 5.67, page 125: For part (a), because 56253, other changes .ÐFÑœÐÎÑÐÑœÎare 76, 1/4, 1859, and 36221. For part (b),.œÎ+œ5œÎ^œÎÐÎÑÐÑ ÐÎÑÐÎќΜ362210.25185221761,3491,326 1.01735.Exercise 5.68, page 125: Write 12 two times in place of .IÐ\l\œÑIÐ\l\œX Ñ#"#"Exercise 5.84, page 133: In the expression for the term in parentheses should be +s divided by 2 and the number 3263should not be squared. The answer is correct.)*Exercise 5.85, page 134: The formula for is correct, however the value is 22,401.00.@s Substituting this correct value into the rest of the development produces 617.54,+œs 5œ^œ^œ^œs 36.27, 0.8585, 0.8663, 0.9330. The three estimates are then"#$203.61, 225.53, and 181.39. For the alternative method, the new values must be used ^and so 204.32 and the three estimates are 204.50, 226.37, and 181.81..s œExercise 5.86, page 135: Change the latter part to read 5,62513,7500.4091,5œÎœs ^œÎœ œ33.40910.8800. The premium is 0.8800(475)0.1200(600)490.。
《北美精算师大纲》word版
基本教育阶段(6门课程)：课程1：精算科学的数学基础说明：这门课程的目的是为了培养关于一些基础数学工具的知识，形成从数量角度评估风险的能力，特别是应用这些工具来解决精算科学中的问题。
并且假设学员在学习这门课程之前已经熟练掌握了微积分、概率论的有关内容及风险管理的基本知识。
主要内容及概念：微积分、概率论、风险管理（包括损失频率、损失金额、自留额、免赔额、共同保险和风险保费）课程2：利息理论、经济学和金融学说明：这门课程包括利息理论，中级微观经济学和宏观经济学，金融学基础。
在学习这门课程之前要求具有微积分和概率论的基础知识。
主要内容及概念：利息理论，微观经济学，宏观经济学，金融学基础课程3：随机事件的精算模型说明：通过这门课程的学习，培养学员关于随机事件的精算模型的基础知识及这些模型在保险和金融风险中的应用。
在学习这门课程之前要求熟练掌握微积分、概率论和数理统计的相关内容。
建议学员在通过课程1和课程2后学习这门课程。
主要内容及概念：保险和其它金融随机事件，生存模型，人口数据分析，定量分析随机事件的金融影响课程4：精算建模方法说明：该课程初步介绍了建立模型的基础知识和用于建模的重要的精算和统计方法。
在学习这门课程之前要求熟练掌握微积分、线性代数、概率论和数理统计的相关内容。
主要内容及概念：模型－模型的定义－为何及如何使用模型－模型的利弊－确定性的和随机性的模型－模型选择－输入和输出分析－敏感性检验－研究结果的检验和反馈方法－回归分析－预测－风险理论－信度理论课程5－精算原理应用说明：这门课程提供了产品设计，风险分类，定价/费率拟定/建立保险基金，营销，分配，管理和估价的学习。
覆盖的范围包括金融保障计划,职工福利计划，事故抚恤计划，政府社会保险和养老计划及一些新兴的应用领域如产品责任，担保的评估，环境的维护成本和制造业的应用。
该课程的学习材料综合了各种计划和覆盖范围以展示精算原理在各研究领域中应用的一致性和差异性。
精算师考试用书 (2)
精算师考试用书简介精算师考试是精算师职业资格认证的重要标准之一。
精算师考试用书是考生参加考试所必备的学习资料。
本文档将介绍精算师考试用书的相关内容，包括选择用书的原则、常用的参考书目等。
选择用书的原则1. 遵循考试大纲在选择精算师考试用书时，要遵循考试大纲。
考试大纲是考试的权威指南，包含了考试的内容、重点和要求。
根据考试大纲的要求，选择适合自己的用书是非常重要的。
2. 综合参考资料精算师考试涉及的内容非常广泛，涵盖了精算学的各个领域，包括保险精算、金融精算、风险管理等。
在选择用书时，可以综合参考多种资料，如教材、教辅资料、学术论文等。
3. 知名出版社选择由知名出版社出版的精算师考试用书是一个不错的选择。
知名出版社通常有严格的审核制度和专业的编辑团队，可以保证用书的质量和准确性。
常用的参考书目以下是一些常用的参考书目，供考生参考：1. 《精算学原理》•作者：邬炜•出版社：人民邮电出版社这本书是精算学的经典教材之一，系统地介绍了精算学的基本原理和方法。
它以理论结合实践的方式，帮助读者理解和应用精算学的相关知识。
2. 《保险精算导论》•作者：林子仁•出版社：中国财政经济出版社这本书是针对考生学习保险精算相关知识的教材。
它详细介绍了保险精算的基本概念、模型和方法，并提供了大量的案例和习题，有助于考生更好地理解和掌握保险精算的知识。
3. 《金融精算学》•作者：郑小明、孙可可•出版社：机械工业出版社这本书介绍了金融精算学的基本概念、理论和方法。
它以实际问题为背景，阐述了金融精算学的应用和实践，对于考生学习金融精算学非常有帮助。
4. 《风险管理与精算学》•作者：陈体盛•出版社：中国人民大学出版社这本书主要介绍了风险管理在精算学中的应用。
它详细讲解了风险管理的基本理论和方法，并提供了大量的实例和案例，有助于考生理解和掌握风险管理和精算学的关系。
选择适合自己的精算师考试用书是考功完成考试的重要因素之一。
在选择用书时，应遵循考试大纲，综合参考多种资料，并选择由知名出版社出版的用书。
Cpnnjfm精算师考试背景材料共10页word资料
七夕，古今诗人惯咏星月与悲情。
吾生虽晚，世态炎凉却已看透矣。
情也成空，且作“挥手袖底风”罢。
是夜，窗外风雨如晦，吾独坐陋室，听一曲《尘缘》，合成诗韵一首，觉放诸古今，亦独有风韵也。
乃书于纸上。
毕而卧。
凄然入梦。
乙酉年七月初七。
-----啸之记。
精算师考试背景材料一、精算师简介精算学精算学在西方已经有三百年的历史，它是一门运用概率论等数学理论和多种金融工具，研究如何处理保险业及其他金融业中各种风险问题的定量方法和技术的学科，是现代保险业、金融投资业和社会保障事业发展的理论基础。
精算师精算师是经过金融保险监管部门认可其从业资格的个人。
在保险公司中，精算师是核心部门的核心人才，有着极高的地位、权力和职责。
精算师在保险公司的主要职责包括：新保险产品开发设计：在保险市场越来越激烈竞争中，只有不断推出符合人们需要的新保险产品才能生存和发展，而精算师是新保险产品的主要设计者。
一个新保险产品的条款、价格设计，既要保证公司能赢利，又要有管理的可行性，更要符合人们需要、定价合理、有市场竞争力。
比如一个寿险产品，精算师必须通过以往的人口寿命统计、现行银行利率和费用率等资料进行计算，设计出投保人的各种限制条款（如健康条件等），对收益支付的可能性及支付时间做出计算，最后与公司管理高层共同确定保单的价格。
而这样的新保险产品设计出来后，还须精算师签字然后才送保险监管部门审批。
保险产品管理：在产品售出后，精算师经常需要参与产品管理。
如果该产品是参与分红的保险，是根据实施时间付给客户年息，则必须分析公司能够并且应该支付的年息量。
这就要求分析该计划的实施状况，以及未来可能需要的资金量。
财务管理：对于大多数保险产品来说，其积累的资金一部分被储备起来供以后支付使用，精算师必须估算储备金的数量，并计算出该计划今后的开支；审核公司的年底财务报告，并在报告上签字；把握投资方向，对公司的各项投资进行评估，以确保投资的安全和收益。
因此，当一名精算师在其意见下签字时，就意味着一个保险计划、一个养老金计划或别的什么许诺已经诞生，对保险公司、国家、社会将产生相当大的影响。
Bhevaba精算师考试共9页
Time will pierce the surface or youth, will be on the beauty of the ditch dug a shallow groove ; Jane will eat rare!A born beauty, anything to escape his sickle sweep.-- Shakespeare精算师精算师（actuary）由保险公司雇用的数学专业人员，主要从事保险费、赔付准备金、分红、保险额、退休金、年金等的计算。
其计算依据来源于理赔参照表，而这份表格是基于本公司和同行索赔的经验及相关统计数据而制定的。
简介精算师(Actuary)，拉丁语意思“经营”，是一种处理金融风险的商业性职业。
精算师采用数学、经济、财政和统计工具主要处理一些与保险、再保险公司相关的不确定的未知事件。
另外，还与雇员保险金（医疗保险和退休金计划）、社会福利工程（社会保障和社会护理）有关。
金融领域对精算师的技能有着大量的需要，尤其是在投资、保险以及养老金领域。
目前，大部分的精算师都会于财产保险公司（Non-life/General insurance）或人寿保险公司(Life insurance)工作。
工作范围包括设计新品种的保险产品，计算有关产品之保费及所需的准备金，为保险公司作风险评估及制定投资方针，并定期作出检讨及跟进。
其余的精算师主要在咨询公司(主要的客户是规模较小的保险公司及银行)、养老金投资公司、医疗保险公司及投资公司工作。
越来越多的其他大型公司也开始雇用精算师进行风险管理工作。
编辑本段工作内容精算师其实保险精算师的工作范围十分广泛，包括：①保险产品的设计：通过对人们保险需求的调查，设计新的保险条款，而保险条款的设计必须兼顾人们的不同需要，具有定价的合理性、管理的可行性以及市场的竞争性；②保险费率的计算：根据以往的寿命统计、现行银行利率和费用率等资料，以确定保单的价格；③准备金和保单现金价值的计算；④调整保费率及保额：根据社会的需要及时间，调整保费率和保障程度，以增加吸引力和竞争力；⑤审核公司的年底财务报告⑥投资方向的把握：对公司的各项投资进行评估，以确保投资的安全和收益；⑦参与公司的发展计划：为公司未来的经济决策提供有效的数据支持和专业建议。
【北美精算师资格考试】ASA---exam-p【考试说明】-----即概率论考试
【北美精算师资格考试】ASA---exam-p【考试说明】-----即概率论考试Probability ExamThe Probability Exam is a three-hour multiple choice examination and is referred to as Exam P by the SOA and Exam 1 by the CAS. The examination is jointly sponsored and administered by the SOA, CAS, and the Canadian Institute of Actuaries (CIA). The examination is also jointly sponsored by the American Academy of Actuaries (AAA) and the Conference of Consulting Actuaries (CCA).The Probability Exam is administered as a computer-based test. For additional details, Please refer to “Computer-Based Testing Rules and Procedures”.The purpose of the syllabus for this examination is to develop knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial scienceis emphasized. A thorough command of the supporting calculus is assumed. Additionally, a very basic knowledge of insurance and risk management is assumed.A table of values for the normal distribution is available below for candidates to download and will beincluded with the examination. Since the table will be included with the examination, candidates will not be allowed to bring copies of the table into the examination room.Check the Updates section on this exam’s home page for any changes to the exam or syllabus.LEARNING OUTCOMESCandidates should be able to use and apply the followingconcepts in a risk management context:1. General ProbabilitySet functions including set notation and basic elements of probabilityMutually exclusive eventsAddition and multiplication rulesIndependence of eventsCombinatori a l probabilityConditional probabilityBayes Theorem / Law of total probability2. Univariate probability distributions (including binomial, negative binomial, geometric,hypergeometric, Poisson, uniform, exponential, gamma, and normal)Probability functions and probability density functionsCumulative distribution functionsMode, median, percentiles, and momentsVariance and measures of dispersionMoment generating functionsTransformations3. Multivariate probability distributions (including the bivariate normal)Joint probability functions and joint probability density functionsJoint cumulative distribution functionsCentral Limit TheoremConditional and marginal probability distributionsMoments for joint, conditional, and marginal probability distributionsJoint moment generating functionsVariance and measures of dispersion for conditional and marginal probability distributionsCovariance and correlation coefficientsTransformations and order statisticsProbabilities and moments for linear combinations of independent random variablesREFERENCESSuggested TextsThere is no single required text for this exam. The texts listed below may be considered as representative of the many texts available to cover material on which the candidate may be examined. Texts are added and deleted as part of a regular process to keep the list up-to-date. The addition or deletion of a textbook does not change the bank of questions available for examinations. There is no advantage to selecting a text recently added or not using a text recently removed.Not all the topics may be covered adequately by just one text. Candidates may wish to use more than oneof the following or other texts of their choosing in their preparation. Earlier or later editions may also be adequate for review. The # indicates new or updated material.A First Course in Probability (Eighth Edition), 2009, by Ross, S.M., Chapters 1–8.Mathematical Statistics with Applications (Seventh Edition), 2008, by Wackerly, D., Mendenhall III, W.,Scheaffer, R.,Chapters 1-7.Probability for Risk Management, (Second Edition), 2006, by Hassett, M. and Stewart, D., Chapters 1–11.Probability and Statistical Inference (Eighth Edition), 2009, by Hogg, R.V. and T anis, E.A., Chapters 1–5.?# Probability andStatistics with Applications: A Problem solving Text, 2010, by Asimow, L. and Maxwell, M.?Probability: The Science of Uncertainty with Applications to Investments, Insurance and Engineering 2001, by Bean, M.A., Chapters 1–9.Study NotesThe candidate is expected to be familiar with the concepts introduced in “Risk and Insurance”.Code TitleTables for E xam P/1Exam P/1Sample Questions and Solutions (1–152)P-21-05Risk and Insurance。
北美精算师资格考试守则介绍-精算师考试.doc
北美精算师资格考试制度介绍-精算师考试SOA从2005年起采用新的教育体制。
获得FSA（精算师）称号必须通过以下课程考试。
ASA（准精算师）资格要求：在新的体系下，SOA要求完成四门初级教育课程考试，VEE 课程,在4门中级教育课程考试中任选两门参加（可选择作论文来冲抵一门课程），并通过准会员职业课程（APC），才能获得准会员资格，也即我们以前说的准精算师资格。
下面分别介绍这些课程考试内容。
（１）初级教育课程考试（PreliminaryEducationExaminations）①ExamP：概率及相关知识考试，考试时间3小时；②ExamFM：金融数理基础，主要是利息理论，考试时间2小时；③ExamM：风险模型，主要涉及人寿保险常用模型，总体损失模型，考试时间4小时；④ExamC：风险模型的建立和评价，涉及模型拟合和可信度理论（Credibilitytheory）,考试时间4小时。
（２）VEE课程（ValidatedbyEducationalExperience）该课程是针对那些在学校已修过相关课程的人士，他们可以凭课程证明获得学分。
对于没有在学校学习过相关课程，或者SOA不认证你所在学校所提供的课程的人士（中国绝大部分学校包括中山大学未获认证），仍然可以通过考试来获得相应的VEE学分。
可密切关注CAS提供的考试（TRANSITIONALEXAMS），通过考试的人仍可以得到VEE的学分。
VEE的课程包括：①应用统计学(AppliedStatisticalMethods)：主要包括回归分析与时间序列两方面内容。
回归分析主要内容：最小二乘法，一元/多元线性模型，模型假设检验，模型拟和优度检验。
时间序列主要内容：线性时间模型，ARIMA模型，数据分析与预测，预测误差与区间估计。
②公司财务(CorporateFinance)：主要包括财务管理与投资学两方面内容。
财务管理主要内容：股份公司定义，资本结构的定义，资本成本的计算，如何确定最优资产/负债结构，资产结构如何影响投资决策。
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P:
指定教材：
Fundamentals of Probability ￥200 1.5 kg
Solution manual of Fundamentals of Probability ￥80
A First Course in Probability, 7th Ed ￥150
考试manual：
ASM版Exam P 9th Edition （2008秋） study manual ￥90 1.5kg
ASM版Exam P 10th Edition （2009春）study manual ￥200 1.5kg ACTEX版 Exam P （2009春）study manual ￥180 1.5kg
GUO版 Exam P （2009春）study manual ￥160 1.5kg
DAR新版Exam P Equation Study List公式手册￥20
FM:
指定教材：
Financial Mathematics ￥70.00 1kg
Mathematics of Investment and Credit, 3rd Edition, 2004 ￥120.00 1kg
Mathematics of Investment and Credit Solutions Manual ￥80 0.5kg The Theory of Interest 2nd Edition ￥55 1kg
Derivatives Markets 2nd edition ￥140.00 2kg （这本书fm mfe c都需要用到）
Derivatives Markets Solution Manual Second Edition ￥80.00 0.5kg 考试manual：
ASM版Exam FM 8th Edition （2008秋） study manual ￥160
ASM版Exam FM 9th Edition （2009春）study manual ￥200 1.5kg ACTEX版 Exam FM （2009春）study manual ￥220 1.5kg
GUO版 Exam FM （2009春）study manual ￥180 1.5kg
DAR新版Exam FM Equation Study List公式手册￥20
MFE：
指定教材：
Derivatives Markets 2nd edition
Derivatives Markets Solution Manual Second Edition
考试manual：
ASM版Exam MFE 8th Edition （2008秋） study manual ￥70 1.5kg ASM版Exam MFE 9th Edition （2009春）study manual ￥180 1.5kg ACTEX版 Exam MFE （2009春）study manual ￥240 1.5kg
GUO版 Exam MFE （2009春）study manual ￥200 1.5kg
MLC：
指定教材：
Actuarial Mathematics, 2nd Edition ￥105.00 2kg
Solutions Manual for Bowers' et al Actuarial Mathematics ￥80.00 0.5kg
Introduction to Probability Models, 8th Edition, 2003 ￥100 1.5kg 考试manual：
ASM版Exam MLC 7th Edition （2008秋） study manual ￥240 2.5kg ACTEX版 Exam MLC （2008春）study manual ￥130 1.5kg
GUO版 Exam MLC （2009春）study manual ￥260 1.5kg
DAR新版Exam MLC Equation Study List公式手册￥30
C：
指定教材：
Loss Models From Data to Decisions ￥90 2kg
Solutions Manual to Loss Models From Data to Decisitions ￥80 0.5kg
Foundations of Casualty Actuarial Science, 4th Edition, 2001 ￥90 1.5kg
考试manual：
ASM版Exam C 8th Edition （2008秋） study manual ￥260 2.5kg ACTEX版 Exam C （2008春）study manual ￥185 1.5kg
GUO版 Exam C (2009春）study manual ￥300 2.5kg
DAR新版Exam C Equation Study List公式手册￥30
Fap：
指定教材，已经全部是最新版的，全套价格为￥900 （非最新版一套为￥600）
Fundamentals of Private Pensions
Understanding Actuarial Management:
Enterprise Risk Management
INVESTMENT SCIENCE
Introduction to Ratemaking&Loss Reserving Third Edition
Group Insurance 5th edition
Actuarial Aspects of Individual Life Insurance 2nd Edition
希望以上资料对你有所帮助，附励志名言3条：
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2、每个人都必须发展两种重要的能力适应改变与动荡的能力以及为长期目标延缓享乐的能力。
3、将一付好牌打好没有什么了不起能将一付坏牌打好的人才值得钦佩。