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Notes-Ch8-331W09

# Notes-Ch8-331W09 - Life Contingencies 1 ACTSC 331 Spring...

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Unformatted text preview: Life Contingencies 1 - ACTSC 331, Spring 2006 Review Notes for Chapter 8 1. The prospective formula for benefit reserves for general fully discrete in- surances on ( x ): h V = ∞ X j =0 b h + j +1 v j +1 j p x + h q x + h + j- ∞ X j =0 π h + j v j j p x + h , h = 0 , 1 , 2 , ..., where b j +1 is the death benefit in the ( j + 1)-th policy year if death is in the ( j + 1)-th policy year and payable at the end of the policy year of death, and π j is the benefit premium in the ( j + 1)-th policy year and payable at the beginning of the policy year as long as ( x ) is alive, j = 0 , 1 , 2 , .... 2. The retrospective formula for benefit reserves for general fully discrete in- surances on ( x ): h V = 1 h E x h- 1 X j =0 π j v j j p x- h- 1 X j =0 b j +1 v j +1 j p x q x + j , h = 0 , 1 , 2 , .... 3. The prospective formula for benefit reserves for general fully continuous insurances on ( x ): t ¯ V = Z ∞ b t + s v s s p x + t μ x ( t + s ) ds- Z ∞ π t + s v s s...
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Notes-Ch8-331W09 - Life Contingencies 1 ACTSC 331 Spring...

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