2011_175HWSet4

# 2011_175HWSet4 - Finally apply the Law of Unconscious...

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THE UNIVERSITY OF IOWA 22S:175 H.W. Set #4 Due at the beginning of class on Monday, February 14, 2011 Write legibly. Show your steps. Explain your reasoning. Simplify your answers. Each question is worth 10 points (1) Panjer (1998), Exercise 5.1. (Ignore the last sentence.) (2) Panjer (1998), Exercise 5.6. (3) Panjer (1998), Exercise 5.8. (4) Ross (2010), page 355, Exercise 10(b) Solve this problem as follows: First, note that E[MX|M = Y] = E[YX|X > Y]. Then, note that the RHS is a special case of E[g(X, Y) | X > Y], which can be evaluated as E[ ( , ) ( )] E[ ( )] g X Y I X Y I X Y > > , where I (.) denotes the indicator function.
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Unformatted text preview: Finally, apply the Law of Unconscious Statistician to evaluate the ratio as , , ( , ) ( ) ( , )d d ( ) ( , )d d X Y X Y g s t I s t f s t s t I s t f s t s t ∞ ∞-∞ -∞ ∞ ∞-∞ -∞ > > ∫ ∫ ∫ ∫ = ……. . [Hint: Use (5.5) on page 302 to check your answer for the denominator.] Copying the solution on page 752 is not acceptable for this homework. You should know the difference between effective annual interest rate and continuously compounded interest rate (or force of interest ). If not, look up Appendix B.1 on page 875 of McDonald (2006)....
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