{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment 4 soln

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

This preview shows pages 1–2. Sign up to view the full content.

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 1 1 1 1 K K x x x K L v a v d d + + + π π = − π = + ±± The mean and variance of the loss-at-issue are ( ) ( ) ( ) ( ) { } ( ) 2 2 2 2 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 x x x x E L A d d L A A d π π = + = + = − 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 S L E S n S n = = = − = Hence, we have ( ) ( ) ( ) ( ) 0 0.08 0.08 Pr 0 Pr 0.05 1.645 0.0496 0.0496 Var 20.97. S E S 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, 1 0,1, ,9, 10,11, 10,000 10,11, K K K a K K v K Z Y a K v a K + + + π = + π = = = π = = ±± ±± ±±

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online