Part-4-Notes-232-2010W

Part-4-Notes-232-2010W - Summary of Lecture Notes ACTSC...

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Unformatted text preview: Summary of Lecture Notes ACTSC 232, Winter 2010 Part 4 Benefit Premiums The loss random variable L for an insurance or annuity is defined as L = The PV of benefits- The PV of premiums. The expectation of the loss random variable is E [ L ] = The APV of benefits- The APV of premiums. Equivalence Principle (EP): Set premiums such that E [ L ] = 0 or The APV of benefits = The APV of premiums. Percentile Principle (PP): Set premiums such that Pr { L > } = . Note that we assume the equivalence principle throughout this courses unless otherwise stated. 4.1 Fully continuous benefit premiums In an insurance, the benefits of the insurance form a continuous life insurance while the premiums of the insurance form a continuous life annuity. (a) A fully continuous whole life insurance of 1 on ( x ) with an annual premium rate of P : L = v T x- P a T x , P = A x a x = A x 1- A x = 1- a x a x , V ar [ L ] = 1 + P ! 2 V ar ( v T ) = 1 + P ! 2 h 2 A x- ( A x ) 2 i = 2 A x- ( A x ) 2 ( a x ) 2 . (b) A fully continuous h-Payment whole life insurance of 1 on ( x ) with an annual pre- mium rate of P : L = v T x- P a T x h , P = A x a x : h . 1 (c) A fully continuous n-year term insurance of 1 on ( x ) with an annual premium rate of P : L = v T x- P a T x , T x n- P a n , T x > n P = A 1 x : n a x : n . (d) A fully continuous n-year endowment insurance of 1 on ( x ) with an annual premium rate of P : L = v T x n- P a T x n , P = A x : n a x : n = A x :...
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This note was uploaded on 03/20/2011 for the course ACTSC 232 taught by Professor Matthewtill during the Summer '08 term at Waterloo.

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Part-4-Notes-232-2010W - Summary of Lecture Notes ACTSC...

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