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Unformatted text preview: Review Notes – ACTSC 331, FALL 2011 Part 1 – Policy Values/Benefit Reserves (Continuous Basis) 1. The prospective formula for policy values/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 p x + t ds, t ≥ , where b t is the death benefit at time t if death is at time t , and π t is the annual rate of benefit premiums at t and payable continuously as long as ( x ) is alive, t ≥ . 2. The retrospective formula for policy values benefit reserves for general fully continuous insurances on ( x ): t ¯ V = 1 t E x Z t π s v s s p x ds- Z t b s v s s p x μ x ( s ) ds , t ≥ . 3. Prospective formulas for the standard fully continuous policy values/benefit reserves: (a) Whole life insurance of 1 on ( x ): t ¯ V ( ¯ A x ) = ¯ A x + t- ¯ P ( ¯ A x ) ¯ a x + t , t ≥ . (b) n-Year endowment insurance of 1 on ( x ): t ¯ V ( ¯ A x : n | ) = ¯ A x + t : n- t |- ¯ P ( ¯ A x :...
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This note was uploaded on 01/04/2012 for the course ACTSC 331 taught by Professor David during the Fall '09 term at Waterloo.
- Fall '09