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Homework_Assignment_20

# Homework_Assignment_20 - Homework Assignment 20(1(a If the...

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Homework Assignment 20: (1) (a) If the adjustment coefficient R = 2, find u so that ψ (u) < 0.05. (b) Suppose that X has a Gamma(2,3) distribution and that the adjustment coefficient R = 1. Find θ , the relative security loading. (c) Suppose that X is exponential with mean 2. If ψ (0) = 0.8, what is ψ (1)? (d) Suppose that X is uniformly distributed on [0,4] and that u=5. Given that the surplus eventually drops below 5, what is the probability that, the first time this happens, the surplus is between 3 and 5? (Ans (a) u 1.4979 (b) 7/8 (c) 0.7239 (d) 3/4 ) (2) Do parts (a) and (b) of Exercise 13.21 on page 433. (Ans: (a) (21/10)(e -3x + e -7x ) (b) 29/105) (3) A surplus process has a compound Poisson claims process with 5 claims expected per period and p(x) = (1/4) e -x/4 for x > 0. Initial surplus is 15. Premiums are collected continuously at the rate of 25 per period.

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