Homework_Assignment_11 - The reinsurer wants to collect in...

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Homework Assignment 11: (1) An insurer offers group term insurance on 250 mutually independent lives for a premium of 285. The probability of a claim is 0.02 for each life. The distribution of the number of lives by benefit amount is: Benefit Amount Number Covered 20 100 50 100 100 50 Reinsurance is purchased which costs 120% of expected claims above a retention limit of 40 per life. Using the normal approximation, determine the probability that the total of retained claims and reinsurance premiums will exceed the premium. (Ans 0.348) (2) In problem (1), calculate the retention limit that minimizes the probability that the total of retained claims and reinsurance premiums will exceed the premium. Assume that the limit is between 20 and 50. (Ans 32) (3) An insurance company sold 1-year term life insurance policies on 2,300 lives as shown below: Class Benefit Amount Number Covered Probability of Death 1 1 500 0.10 2 2 500 0.02 3 3 500 0.02 4 2 300 0.10 5 2 500 0.10 The insurance company’s retention limit is 1 unit per life.
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Unformatted text preview: The reinsurer wants to collect in the aggregate an amount equal to the 95 th percentile of the distribution of aggregate ceded claims. Using a normal approximation, determine the reinsurer’s relative security loading. (Ans 0.1645) (4) Rework problem (3) using a lognormal approximation. [The formulas for the mean and variance of a lognormal distribution are in the table on page 704 (we used μ instead of m ). Recall that the natural log of a lognormal random variable is normally distributed with mean μ and standard deviation σ .] (Ans 0.1725) (5) Consider the portfolio of insurance contracts in problem (1). Calculate the expected value of the claims provided by a stop-loss reinsurance coverage where there is a retention amount of 40 on individual policies and the deductible amount on the business retained is 300. (Ans 0.8408, using Excel functions PI, SQRT, EXP, NORMSDIST)...
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This note was uploaded on 05/11/2011 for the course STOR 472 taught by Professor Charlesdann during the Spring '11 term at University of North Carolina School of the Arts.

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