Test_2_-_Solutions_-_F08

# Test_2_-_Solutions_-_F08 - ACTSC 331 - Life Contingencies I...

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Test 2 1. ( 8 marks ) Consider a special fully continuous whole life insurance contract issued to ( x ) . The b T b T = 200 e & 0 : 02 T , 0 < T < 20 200 e & 0 : 02(20) , T > 20 , while the premium payable at time t , say t , is t = , t & 0 . We have (1) A x A 1 x : 20 j @ ± = 3% 0.5 0.35 @ ± = 5% 0.38 0.3 @ ± = 7% 0.3 0.26 (2) 20 p x = 0 : 55 (3) v t = e & 0 : 05 t , t & 0 . Determine under the equivalence principle. Solution: Z = b T v T , T > 0 = 200 e & 0 : 02 T e & 0 : 05 T , 0 < T < 20 200 e & 0 : 02(20) e & 0 : 05 T , T > 20 = 200 e & 0 : 07 T , 0 < T < 20 200 e & 0 : 02(20) e & 0 : 05 T , T > 20 . Z can be decomposed as Z = Z 1 + Z 2 , where Z 1 = 200 e & 0 : 07 T , 0 < T < 20 0 , T > 20 , and Z 2 = 200 e & 0 : 02(20) ± & 0 , 0 < T < 20 e & 0 : 05 T , T > 20 . 1

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## This note was uploaded on 10/30/2009 for the course ACTSC 331 taught by Professor David during the Spring '09 term at Waterloo.

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Test_2_-_Solutions_-_F08 - ACTSC 331 - Life Contingencies I...

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