Exercises_-_Chapter_8

Exercises_-_Chapter_8 - ACTSCI 331 Life Contingencies I...

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ACTSCI 331 - Life Contingencies I Exercises (Chapter 8) 1. A special fully discrete whole life insurance is issued to (40). The death bene°t payable at the end of the year of death and the premium paid by the insured at the beginning of the year (if alive) are respectively b K +1 = ° 1000, K = 0, 1, ..., 24 500, K = 25, 26, ... and ° k = 8 < : 3 °; k = 0, 1, ..., 14 2 ° , k = 15 , 16, ...29 0, k = 30 , 31, ... : Given that k A 40+ k A 1 40+ k : 25 ° k j ° a 40+ k : 15 ° k j ° a 40+ k : 30 ° k j 0 0.202 0.114 10.005 13.414 10 0.316 0.149 4.386 10.806 20 0.458 0.112 ± 6.929 40 0.744 ± ± ± , (a) de°ne the loss r.v. j L for all possible values of j (b) compute ° under the equivalence principle and the bene°t reserves 10 V , 20 V and 40 V . (Answers: 4.29, 120.97, 225.55, 372) 2. A special whole life insurance is issued to (35) with the following embedded components: (1) death bene°t payable at the end of the ( k + 1 ) year = b k +1 = 50( k + 1 ), k = 0, 1, ...; (2) level bene°t premium payable at the beginning of each year for at most 25 years (if alive) Using (1) 10 V 35 = 0.111; (2) ( IA ) 35 = 3.352; (3) A 35 = 0.142; (4) ( IA ) 45 = 4.191; (5) 10 V 35: 25 j = 0.227. , calculate the bene°t reserve at time 10. (Answer: 198.62) 3. A fully discrete whole life insurance issued to (30) has the following characteristics : (1) b k +1 = e 0 : 06( k +1) , k = 0, 1, 2, ...; (2) v k +1 = e ° 0 : 08( k +1) , k = 0, 1, 2, ... . . The bene°t premium is paid as long as the insured is alive at the beginning of each year. Under a speci°c mortality assumption, we have 10 V 30 A 30 A 40 @ ± = 2% 0.094 ? 0.688 @ ± = 6% 0.045 0.359 ?
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