PQ-1-Answer-331-2011-F

PQ-1-Answer-331-2011-F - +1-5 + (0 . 05 P + 120) a K 35...

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Answers to Practice Questions 1 – ACTSC 331, FALL 2011 1. (a) By the equivalence principle, we have 50 , 000 A 1 [41]: 3 = P ¨ a [41]: 3 and hence P = 80 . 90. (b) Given that the woman is still alive after one year or given that K [41] 1, 1 L = 50 , 000 v K [41] +1 - 1 - P ¨ a K [41] +1 - 1 , K [41] 2 , - P ¨ a 2 , K [41] 3 . (c) The policy value is 1 V = 50 , 000 A 1 [41]+1: 2 - P ¨ a [41]+1: 2 = 29 . 16. (d) Note that V ar ( 1 L | K [41] 1) = E ( 1 L 2 | K [41] 1) - ( 1 V ) 2 . Furthermore, if K [41] - 1 = 0 | K 41 1, then 1 L = 50 , 000 v - P ¨ a 1 = 47088 . 90 with probability q [41]+1 = 0 . 00187583; if K [41] - 1 = 1 | K 41 1, then 1 L = 50 , 000 v 2 - P ¨ a 2 = 44342 . 60 with probability p [41]+1 q [41]+2 = 0 . 00219683; and if K [41] - 1 2 | K 41 1, then 1 L = - P ¨ a 2 = - 157 . 22 with probability 2 p [41]+1 = 0 . 995927. Thus, E ( 1 L 2 | K [41] 1) = 8503568 . 83 and the standard derivation is q V ar ( 1 L | K [41] 1) = 2915 . 94 . 2. (a) Let the gross premium be P . By the equivalence principle, 300 , 000 A 35 +(0 . 05 P + 120)¨ a 35 + 0 . 35 P + 255 = P ¨ a 35 and thus P = 2852 . 81. (b) The gross premium policy value is 1 V = 300 , 000 A 36 +(0 . 05 P +120)¨ a 36 - P ¨ a 36 = 814 . 08. (c) Given that K 35 5, 5 L = 300 , 000 v K 35
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Unformatted text preview: +1-5 + (0 . 05 P + 120) a K 35 +1-5-P a K 35+1-5 . Thus, V ar ( 5 L | K 35 5) = 300 , 000-120-. 95 P d 2 V ar ( v K 35+1-5 | K 35 5) = 300 , 000-120-. 95 P d 2 V ar ( v K 40 +1 ) = 2 . 70252 10 9 . (d) Let the net premium be . By the equivalence principle, 300 , 000 A 35 = a 35 and thus = 2508 . 74. (e) The net premium benet reserve is 1 V = 300 , 000 A 36- a 36 = 2058 . 89. (f) In this case, given that K 35 5, 5 L = 300 , 000 v K 35 +1-5- a K 35 +1-5 and hence V ar ( 5 L | K 35 5) = 2 . 68008 10 9 . 3. 1 V 1 97: 3 = A 1 98: 2-P 1 97: 3 a 98: 2 =-. 0826. 4. (a) = A 50 + A 1 50: 5 a 50: 10 + 0 . 5 a 50: 5 . (b) 5 V = A 55- a 55: 5 . (c) 15 V = A 65 . 1...
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