Notes-Ch7-331W09

# Notes-Ch7-331W09 - Review Notes for Chapter 7 ACTSC 331...

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Unformatted text preview: Review Notes for Chapter 7 - ACTSC 331, Winter 2009 1. Prospective principle for continuous benefit reserves: Benefit reserve at time t ≥ = Actuarial present value ( APV ) at time t of the future benefits after time t or from age x + t- APV at time t of the future premiums after time t or from age x + t, given that T ( x ) > t or ( x ) is still alive at time t. 2. General notation for a continuous benefit reserve: t ¯ V for t ≥ 0 and t ¯ V = E [ t L | T ( x ) > t ] , where t L is the prospective loss function at time t or the present value at time t of the future loss after time t , given T ( x ) > t , and t L is defined as t L = the present value at time t of the future benefits after time t- the present value at time t of the future premiums after time t, given T ( x ) > t. 3. Aggregate Mortality Law: T ( x )- t | T ( x ) > t = d T ( x + t ) , where = d means that equality in distribution . 4. Prospective loss functions and prospective formulas for fully continuous benefit reserves: (a) Whole life insurance of 1 on ( x ): t L = v T ( x )- t- ¯ P ( ¯ A x ) ¯ a T ( x )- t | , t ¯ V ( ¯ A x ) = ¯ A x + t- ¯ P ( ¯ A x ) ¯ a x + t . (b) n-Year term insurance of 1 on ( x ): If t < n t L = v T ( x )- t- ¯ P ( ¯ A 1 x : n | ) ¯ a T ( x )- t | , T ( x ) ≤ n ,- ¯ P ( ¯ A 1 x : n | ) ¯ a n- t | , T ( x ) > n , if t = n, t L = 0 . t ¯ V ( ¯ A 1 x : n | ) = ¯ A 1 x + t : n- t |- ¯ P ( ¯ A 1 x : n | ) ¯ a x + t : n- t | , t < n , , t = n . 1 (c) n-Year endowment insurance of 1 on ( x ): If t < n t L = v T ( x )- t- ¯ P ( ¯ A x : n | ) ¯ a T ( x )- t | , T ( x ) ≤ n , v n- t- ¯ P ( ¯ A x : n | ) ¯ a n- t | , T ( x ) > n , if t = n, t L = 1 . t ¯ V ( ¯ A x : n | ) = ¯ A x + t : n- t |- ¯ P ( ¯ A x : n | ) ¯ a x + t : n- t | , t < n , 1 , t = n . (d) h-Payment years, whole life insurance of 1 on ( x ): If t ≤ h t L = v T ( x )- t- h ¯ P ( ¯ A x ) ¯ a T ( x )- t | , T ( x ) ≤ h , v T ( x )- t- h ¯ P ( ¯ A x ) ¯ a h- t | , T ( x ) > h , if t > h, t L = v T ( x )- t ....
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Notes-Ch7-331W09 - Review Notes for Chapter 7 ACTSC 331...

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