Assignment 2

# Assignment 2 - FIN 3220A Actuarial Models I First Term...

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1 FIN 3220A Actuarial Models I First Term 2005-2006 Assignment 2 Hand in the solutions on or before 31 October 2005. 1. A 2-year term insurance is issued to (30). Benefit are payable at the end of the year of death. The death benefit for policy year t is b t . You are given the following: 30 2 1 1 2 31 0.1, 10 , 0 , 10, 0.6, 0. qb b b b qi == ≤= = Find the value of b 1 which minimizes Var( Z ). 2. An insurance is issued to ( x ) that pays 1,000 at the end of n years if ( x ) is alive, and returns the single premium π at the moment of death if ( x ) dies during the first n years. The variance of the present value random variable at issue can be written as () ( ) ( ) ( ) 22 21 2 2 1 1 2 1 :: 1,000 1,000 . xn AA K −π + Determine K . 3. A whole life insurance of 50 is issued to ( x ). The benefit is payable at the moment of death. The p.d.f. of the future lifetime, T , for ( x ) is 5000 0 100 . 0o t h e r w i s e tt ft ≤≤ = The force of interest is 0.10. Calculate the net single premium (i.e. APV ).

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Assignment 2 - FIN 3220A Actuarial Models I First Term...

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