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# Life_Tables - Life Insurance and Superannuation Models Week...

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Life Insurance and Superannuation Models Week 5: Life Tables March 26, 2011 1 / 12

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Week 5: Life Tables Summary Life Tables. Practical ways of assigning numerical probability of death. Actuarial present values ( APV ) Actuarial symbols and notation Insurance payable at the moment of death Continuous Level benefits, varying benefits (e.g. increasing, decreasing) Insurances payable at the end of year of death Discrete Level benefits, varying benefits (e.g. increasing, decreasing) References Chapter 4 (Bowers, et al.) or Chapter 3 (Gerber) ACTL3002: Week 5 2
Assumptions Assume knowledge of the key survival models, the fundamental ones being t q x = integraldisplay t 0 s p x μ x + s ds (1.1) t p x = integraldisplay t 0 - μ x + s ds (1.2) t p x is the probability that a life aged x dies within t years. t q x is the probability that a life aged x survives for at least another t years. μ x + s is the annual rate of transfer between alive and dead at exact age x + s , that the annual rate at which living people are dying at that exact age. ACTL3002: Week 5 3

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Assumptions cont... Think of this as μ x + s ds is the probability of a life aged x + s dying over the very small time interval x + s , x + s + ds For example s p x μ x + s ds is the probability of a life aged x living s years and then dying in the next instant of time Such that t q x is the probability that a life aged x dies at any of the possible moments over t he next t years.
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