风险管理和保险基础 第01章

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人身损失风险 personal loss exposures
• 由于所有的损失最终 都是要由人来承受的， 因此，从某种意义上 说，所有的风险损害 对象都是个人。但是 有一些损失更直接地 影响到人身。
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财产损失风险 property loss exposures
• 因财产发生损毁、灭 失和贬值而使财产的 所有权人遭受损失。 这种损失既有direct loss直接损失，也有 consequential loss引 致损失。
P (Liabilities > Assets)
Answer: 1 - .672 = .338
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Example (Cont): Suppose that an insurance company insures the following group of policies: 100 satellites, each with i = = $10m (for all i) and i = = 100m. Let Xi denote the random loss for satellite i.
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有形风险因素
• Physical hazards are the tangible conditions of the environment that affect the frequency and/or severity of loss. • 导致损失发生的物质方面的因素。如财 产所在的地域、建筑结构和用途等。
两个概念
• speculative risk • pure risk
投机风险: 纯粹风险： 既存在损失的可能性 只有损失机会而无获 又存在获利的可能性。 利机会。 • 三种可能： • 两种可能： 损失、无变化或获利。 损失、无损失。
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§1.2 对待风险的态度
态度 Attitudes Toward Risk
观测次数 1 2 3 4 5 6 7 8 损失值 $100 100 100 500 500 1,000 1,000 1,000 $4,300 损失类型 观测总数 $100 500 1,000 3 2 3 8 概率 3/8=0.375 2/8=0.250 3/8=0.375 8/8=1.000
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(1)均值
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Var aX a Var X
Properties of Variances: 2
Var X Y Var X Var Y 2Cov X ,Y Var aX bY a Var X b Var Y 2abCov X ,Y
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The Covariance 协 方 差 measures the relationship between two random variables. It is computed as Cov (X, Y) = S pi (xi -x) (yi -y) = x,y = E[(x - x)(y -y)] E [(x -x)(y -y)] = E(XY) -xy Cov (X, X) = Var(X) The correlation coefficient between X and Y is computed as r = x,y/ xy
Pooled Losses $0 $2,500 $2,500 $5,000 E(Loss) = $500 Std (Loss) = 707.10
Avg Losses $0 $1,250 $1,250 $2,500
Prob 0.64 0.16 0.16 0.04
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2 Individuals
$0
$500
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风险定义的三个要点
• (1) risk is a state. 风险是一种状态。不论 人们是否意识到，风险都是客观存在的。 • (2)risk has something to do with loss. 风险 是与损失相关的状态。 • (3)uncertainty. 损失的发生具有不确定性。
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无形风险因素
• Attitudes and culture (nonphysical conditions) also affect the probability and severity of loss. • 文化、习俗和生活态度等非物质形态的 因素也会影响损失发生的可能性和受损 的 程 度 。 它 包 括 道 德 风 险 因 素 moral hazard和行为风险因素morale hazard两种。
风险厌恶 Risk Averse
风险中性 Risk Neutral
风险追求 Risk Seeker
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§1.3 风险的度量
• 损失发生的频率 frequency ↑,风险↑ • 损失发生的严重程度 severity↑，风险↑
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• 损失的不确定性和损 失的严重性，构成了 人们对风险的重视程 度。
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损失概率
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风险因素结构图
风险因素 HAZARDS
有形风险因素
无形风险因素
第一部分 风险管理和保险基础
• 第1章 第2章 第3章 第4章 第5章 风险 风险管理 保险 影响保险合同的基本因素 保险合同的内容及其分析
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第一章 风险
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§1.1 风险的本质
• Risk: variability in future outcomes ， which means outcomes may differ from expectations. • 风险是一种客观存在的、损失的发生具 有不确定性的状态。
For any e > 0, Pr[ L > e] .
0 as N
∞.
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Risk Pooling Example
Consider 1 individual, facing the following loss distribution: Loss $0 Prob 0.8
$2,500
0.2
E(Loss) = $500 Std (Loss) = 1,000
2 2 2
E X
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n standard deviation标准差 (Xi-X)2 /n i 1 coefficient of variance离散系数 标准差/均值
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• 相同的均值,标准差 ↑,则风险↑。 • 不同的均值, 则看 coefficient of variance 离散系数。离散系数 ↑,则风险↑。
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责任损失风险 liability loss exposures
• 人们的过失或侵权行 为造成他人的财产损 毁或人身伤亡，在法 律上负有经济赔偿责 任或对此进行申诉。
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PERILS 风险事故
• Perils are the immediate causes of loss. • 风险事故是损失的直接原因，如火灾、 地震、洪水、龙卷风、雷电、盗窃、死 亡、爆炸、疾病等等。 • 可分为人为、自然风险事故和insurable可 保、noninsurable不可保风险事故。
2 2
Var X Y Z Var X Var Y Var Z 2Cov X , Y 2Cov X , Z 2Cov Y , Z Cov aX , bY abCov X ,Y
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Cov(X,X)= Var(X) Cov(Y,X)
Avg Losses 0 833.33 833.33 833.33 1,666.67 1,666.67 1,666.67 2,500.00
Prob 0.512 0.128 0.128 0.128 0.032 0.032 0.032 0.008
E(Loss) = $500 Std (Loss) = 577.35
风险事故 perils
风险因素 hazards
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EXPOSURES 风险载体
• the property or person facing a condition in which loss or losses are possible. • 按照exposure风险载体来分类，风险可 以分为人身损失风险、财产损失风险与 责任损失风险。
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HAZARDS 风险因素
• Hazards are the conditions that lie behind the occurrence of losses, increasing the probability of losses, their severity or both. • 促使和增加损失发生的频率或严重程度 的任何条件。 • 有两类风险因素：有形风险因素physical hazards和无形风险因素intangible hazards.
What is the probability that the insurance company goes under insolvency?
P (Liabilities > Assets)
Answer: .5
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Suppose that the load is 10% instead. P= 11.
$1百度文库000
$1,500
$2,000
$2,500
$3,000
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Suppose that 3 individuals, facing the same loss distribution.
Pooled Losses 0 2,500 2,500 2,500 5,000 5,000 5,000 7,500
• 根据概率分布，可计算样本平均数
样本平均数
X
i 1
n
i
/n
式中，Xi 第i个观察的值 n 观测总数 EX


pX
i
i
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(2)变化性
range差额 可能结果的最大和最小值之差 n variance方差 (Xi-X)2 /n i 1
EX
2
E X pi x 2
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大数定律 LAW OF LARGE NUMBERS
• As a sample of observations is increased in size, the relative variation about the mean declines.
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The Law of Large Numbers
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Suppose that the load is 10% instead. P = 11.
P (Liabilities > Assets) = P ( Z > 1) = 1 - .841345 = .1586
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§1.4 纯粹风险的要素
纯粹风险 pure risk
风险载体 exposures
Cov(X,Y)
Cov(Y,Y)=V ar(Y) Cov(X,Z)
Cov(Y,Z) Cov(Z,Z)
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Cov(X,X)
Cov(Y,X) Cov(Z,X)
Cov(X,Y)
Cov(Y,Y) Cov(Z,X)
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An Example:
Suppose that an insurance company insures the following group of 20 policies:
20 satellites, each with i = = $10m (for all i) and i = = 100m. Let Xi denote the random loss for satellite i.
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Suppose that the insurance company required actuarially fair premiums in exchange for full insurance.
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1 Individual
0.9 0.8 0.7
0.6
0.5 0.4
0.3
0.2 0.1
0.0
$0 $500 $1,000 $1,500 $2,000 $2,500 $3,000
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Suppose that 2 individuals, facing the same loss distribution.