Assignment 4 soln

Assignment 4 soln - FIN 3220A Actuarial Models I First Term...

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1 FIN 3220A Actuarial Models I First Term 2005-2006 Solutions to Assignment 4 1. For this policy, the loss-at-issue random variable is 11 1 1 KK xx x K Lv a v dd ++ + π π ⎛⎞ =− π = + ⎜⎟ ⎝⎠ ±± The mean and variance of the loss-at-issue are () {} 2 2 22 0.019 0.019 1 1 0.19 0.08, 0.057 0.057 0.019 Var 1 1 0.064 0.19 0.0496. 0.057 x x EL A LA A d ππ ⎛⎞ ⎛⎞ =+ − =+ = π = Let n be the number of policies sold. Then we have the aggregate loss, its mean and variance are () () 1 , 0.08 and Var 0.0496 . n i i SL E S n S n = == = Hence, we have 00 . 0 8 0.08 Pr 0 Pr 0.05 1.645 0.0496 0.0496 Var 20.97. SES n n S n S n ⎧⎫ −− ⎪⎪ >= > ⎨⎬ ⎩⎭ ⇒≥ And we must sell at least 21 policies. 2. Let π be the premium. The present value of benefit and present value of future premium random variables are: 1 1 10 10 10 1 0,1, ,9, 10 , 1 , , 9 , 10,11, 10,000 10,11, K K K aK Kv K ZY va K + + −+ π= = ⎨⎨ = The loss-at-issue random variable is L = Z Y . Hence, the premium is given by () ( ) 1 55 10 55:10 55:10 55 1 55:10 55:10 10,000 0 10,000 10,000 12 8 7,272.72.
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This note was uploaded on 05/21/2011 for the course FIN 3220 taught by Professor Cswong during the Spring '05 term at CUHK.

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Assignment 4 soln - FIN 3220A Actuarial Models I First Term...

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