n insurance company wants to offer a new 5-year, level-term life insurance policy to recent college graduates. The policy will have a face value (the amount paid in case of death) of $50,000. Normally, the company charges different premiums depending on the age, gender, tobacco habits and health of the person to be insured*. However, for this simple policy, the company plans to charge a flat $60/year for every eligible customer, and avoid the underwriting costs normally associated with new policies. It costs the company an average of $30 per policy for advertising, sales and administration. In order to estimate the profitability of the new policy, you have been asked to simulate expected policy income (premium payments received) compared to costs (administrative/sale cost plus the occasional death benefit) for an anticipated 100,000 policies.
Background Information:
In each of the 5 policy years, there are 3 possible outcomes.
• The insured may die, and $50,000 will be paid out (there is a 0.1% chance of death in any one year for persons in this age group)
• The insured may decide to drop the policy, with no payout, and all premiums paid so far are forfeited – (there is a 4% chance of this happening during any year)
• The insured may continue to pay the annual premium and the policy remains in force. At the end of the fifth year, the insurance terminates, with no further costs to either party.
Use a Monte Carlo simulation to solve this problem. Rather than a closed-form solution, Monte Carlo techniques depend on setting up the problem parameters and then inputting a series of random values. The combination of all the random solutions is taken as the problem solution.
Hints:
Set up the calculations for cash flow each year based on the costs and probabilities given above. Then, the actual cash flow for each policy (each simulation) depends on random numbers which determine which of the possible events actually occurs for that policy holder during that year. Sum the company’s total expected income for all the policies sold, compare this to the cost of selling the policies, and determine how profitable this will be for the company. (You can ignore the cost of money and treat all income as the same, no matter what year it happens.)
To generate random numbers, use the rand() function found in . It does not take any arguments, and it returns an integer between 0 and RAND_MAX (a constant already defined in the stdlib header). You will want to initialize, or “seed”, the random number function once, at the beginning of your program, by calling srand(time(NULL)). To use the time() function you must also include . Test your program for small numbers of random inputs, and hand-verify proper operation before you scale it up to the full 100,000 policies. Run the program multiple times and observe any differences in the results. If there are differences, what do you think caused them and what does that mean for your analysis?
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