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Math 472 Spring 2011 Class Project

# Math 472 Spring 2011 Class Project - MATH 472/567 ACTUARIAL...

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MATH 472/567: ACTUARIAL THEORY II/TOPICS IN ACTUARIAL THEORY I SPRING 2011: CLASS PROJECT INFORMATION (Due May 4, 2011) Background A few years ago, business mogul Mr. James Claimeron founded The Terminsurer . The Terminsurer is a life insurance company that sells various term insurance products to the public. One type of term insurance sold by The Terminsurer has the following features: The term of the insurance is 20 years. The insured can be either male or female, and have an issue age between 20 and 80. The death benefit is payable at the end of the year of death of the insured. The death benefit amount at time 0 (face value of the policy) is adjusted for inflation each year at an annual effective rate. The policyholder pays annual level contract (gross, expense-loaded) premiums at the beginning of the year. The amount of each contract premium is determined using the equivalence principle. There are various expenses associated with the coverage, each of which are incurred at the beginning of the year: 1. Per-Policy Expenses: an issue expense, and an annual level maintenance expense. 2. Percent-of Premium-Expenses: a first-year commission expense, an annual level renewal-year commission expense, an annual level tax expense, and an annual level profit expense (a loading to attain a fixed profit margin each year). All cash flows are subject to an annual effective interest rate. In addition to death, there is another decrement: withdrawal. Withdrawal ends coverage immediately: future benefits, premiums, and expenses are all zero (note: this also means there is no withdrawal benefit). It is assumed that withdrawal can only occur at the end of each year at a constant rate. Both death and withdrawal have to be survived in order for the term insurance policy to remain in force. 1

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