Part-1-continuous-331-2011-F

Part-1-continuous-331-2011-F - Review Notes ACTSC 331 FALL...

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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 0 b t + s v s s p x + t μ x ( t + s ) ds - Z 0 π t + s v s s p x + t ds, t 0 , 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 0 . 2. The retrospective formula for policy values benefit reserves for general fully continuous insurances on ( x ): t ¯ V = 1 t E x Z t 0 π s v s s p x ds - Z t 0 b s v s s p x μ x ( s ) ds , t 0 . 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 0 . (b) n -Year endowment insurance of 1 on ( x ): t ¯ V ( ¯ A x : n | ) = ¯ A x + t : n - t | - ¯ P ( ¯ A x : n | ) ¯ a x + t : n - t | , 0 t < n, 1 , t = n.
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