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Lecture 2

Actuarial Science 2427A/B Lecture 2: Actuarial Science 2427A/B Lecture : Actuarial Science 2427A/B Lecture : Actuarial Science 2427A/B Lecture : Actuarial Science 2427A/B Lecture : Actuarial Science 2427A/B Lecture : Chapter 2.1Exam


Department
Actuarial Science
Course Code
AS 2427A/B
Professor
Shu Li
Lecture
2

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Chapter 2: Survival Models1
2.1 Future lifetime random variable Tx
Objective: Represent the future lifetime of an individual as a random variable (r.v.)
1. Notation and definitions
(x)=anindividuallifecurrentlyagedx
ω=limitingage(ageatwhichtherearenosurvivors)
Tx=continuousr.v.forfuturelifetimeof(x)
x+Tx=theageatdeathr.v.for(x)
Fx(·)=cumulativedistributionfunction(c.d.f.) forTx
also referred to as the lifetime distribution for (x)
Fx(t)=P[Txt]=P[(x)diesbeforeoratagex+t]
Sx(·)=survivalfunction
Sx(t)=1Fx(t)=P[Tx>t]=P[(x)survivesatleasttyears]
fx(·)=theprobabilitydensityfunction(p.d.f.) forTx
2. Key Formulas
P(Txt)=P(T0x+t|T0>x)(1)
Fx(t)=F0(x+t)F0(x)
S0(x)(2)
S0(x+t)=S0(x)Sx(t)(3)
Sx(t+u)=Sx(t)Sx+t(u)(4)
[TBC]
1Note that lecture note handouts may have to be modied in class to properly reect full notation.
These posted notes may be updated as we work through the material.
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