寿险精算公式汇总
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1.(x)=1-F ()=P (X>x)
>=0x X r S r x x 生存函数: 2.我们约定:x (0)=0,S (0)=1;x F 3.r ()(X>y )=
()X X S y P X x S x > 4.
=Pr(T(x)>t)=Pr(X>x+t )
(+)=()t x X
X p X x S x t S x >
5.
++q =Pr[t =-=-x t u t u x t x t x t u x q q p p ≤ 6. 0 =exp[-(y)dy]=exp[-(x+s)ds]x t t t x x p μμ+?? 7.()f (t)=p x+t t ;T x t x μ ?≥() 0 8. ) 1( x x dl x l dx μ=- 9. +1x s s x x x l p s q l ==-? 10. ()1-11s 1111x x x x s x s s s x x s s s q p q q p q q ++--?--?=-==-?-? 11.常值死力假定:x+=-ln s x p μ 12. 1111111(1)1(1)x s x s x x x x x s x x x l p l s p s p s q l l l l +-++++????==+-=+-=-- ??? ????? 13.1 :0 =(t)dt n t x n t x x A v p μ??? 14. n 年定期死亡保险: ()()2211::x n x n Var Z A A =- 15. n 年期生存保险:()()2211::x x n n Var Z A A =- 16.延期保险:= (t)dt t m x t x x m A v p μ∞??? 17.递推公式:1121 2221:+1:-1:+1:-1=+; =+x x x x x n x n x n x n A vq vp A A v q v p A ()。 18.1:x n x x n x n A A E A +=+ 19. m x x m k x x k m k k X m A E q p v A ++∞=+== ∑1| 20.11:++:()=(IA)+x x x x n x n n n IA A A +?((IA )n ) 21.-1 1 1::=0 (IA)k+n k x n x n k A =∑(1) 22. x i /A Ax δ = 23./x x x A M D = 24.1+x :A =-/x x n x n (M M )D 25.1:+n =/x x x n A D D 26.1++:--(IA)=x x n x n x n x R R n M D ? 27.0=x t x a E dt ∞? 28.1=+x x a A δ 29. ()()()22221δδδx x T T T A A Var Var a Var v v -==???? ??-= 30.ar(+)=0T T V a δυ 31.:0n t t x x n a v p dt =? 32.22:::2 ()()()x n x n x n Var Y a a a δ=-- 33. ::=1x n x n A a δ+ 34.:=x n x x n a a a + 35.11x x x a vp a +=+&&&& 36.:1:1 1x x n x n a vp a +-=+&&&& 37.1(1)x x ia i A =++ 38.x +1x a a =&& 39. +:-=x x n x n x N N a D && 40.x x ()=x A P A a 41.x :()= h x x h A P A a 42.x 1-()=x x a P A a δ 43.x ()=1-x x A P A A δ 44.11 :::x n x n x n A P a =&& 45.1:+:P =P (1)x n x x x n n n P A +- 46.1~:..:1 P =x n x n n P s + 47.++()=-()x x t x t x t V A A P A a 48.+++-()()= x t x x t x t x t M P A N V A D 49.111::-:+:-()=[()-()]x n x t n t x n t x t n t V A P A P A a + 50.++k +=x k x x k x x k M P N V D - 51...111:k :+k:-k :-k 1 k :=A -<;=0=.x n x n x n x k n x n V P a k n V k n +