Midterm_1_-_Solutions-_F08

Midterm_1_-_Solutions-_F08 - ACTSC 331 - Life Contingencies...

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Unformatted text preview: ACTSC 331 - Life Contingencies I Fall 2008 Test 1 1. ( 15 marks ) A fully continuous 20-year pure endowment of $500 is issued to (45). The bene&t premium 500 P ( 20 E 45 ) is 13.94. Given that (1) 2 A 60: 1 5 j & A 60: 1 5 j ! 2 = 0 : 034 (2) 2 A 60: 5 j & & A 60: 5 j 2 = 0 : 003 (3) A 60: 5 j = 0 : 79 (4) & = 5% (5) 5 p 60 = 0 : 8 (a) (2 marks) de&ne the prospective loss r.v. 15 L Solution: De&nition of 15 L 15 L = ( & 500 P ( 20 E 45 ) a T & 15 j , 15 < T < 20 500 v 5 & 500 P ( 20 E 45 ) a 5 j , T > 20 = ( & 13 : 94 a T & 15 j , 15 < T < 20 500 v 5 & 13 : 94 a 5 j , T > 20 (b) ( 3 marks ) &nd the bene&t reserve at time 15 Solution: 500 15 V ( 20 E 45 ) = 500 5 E 60 & 13 : 94 a 60: 5 j = 500 5 E 60 & 13 : 94 1 & A 60: 5 j : 05 = 500 (0 : 8) e & : 05(5) & 13 : 94 1 & : 79 : 05 = 252 : 97 (c) ( 8 marks ) calculate V ar ( 15 L j T > 15) 1 Solution: The prospective loss 15 L can be written as 15 L = 500 15 Z & 13 : 94 & 1 & 15 W & , where 15 Z = , 15 < T < 20 v 5 , T > 20 , and 15...
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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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Midterm_1_-_Solutions-_F08 - ACTSC 331 - Life Contingencies...

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