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?
please write this in C. Thanks
To estimate the profitability of the new insurance policy, you need to simulate the expected policy income compared to the costs. Here's how you can approach this using a Monte Carlo simulation:
1. Set up the problem parameters:
- Determine the face value of the policy ($50,000).
- Define the annual premium for each eligible customer ($60/year).
- Calculate the average cost per policy for advertising, sales, and administration ($30).
2. Calculate the cash flow for each policy year:
- Year 1: Multiply the number of policies (100,000) by the annual premium ($60) to calculate the expected policy income. Adjust this value based on the probabilities of the insured dying (0.1%) or dropping the policy (4%). Calculate the occasional death benefit based on the number of deaths. Subtract the administrative/sale cost per policy.
- Repeat this calculation for years 2, 3, 4, and 5, adjusting the probabilities for dropping the policy based on each year's cumulative dropout rate (e.g., if 4% dropped in year 1, the cumulative dropout rate for year 2 would be 4% of the remaining policies).
3. Perform the Monte Carlo simulation:
- Initialize the random number generator by calling srand(time(NULL)) at the beginning of your program.
- Iterate through each policy and each policy year.
- Generate a random number using rand() to determine which outcome occurs (death, dropout, or policy continuation) based on the probabilities for that year.
- Adjust the cash flow and update the relevant variables based on the outcome.
- Repeat this process for all policies and all years.
4. Calculate the company's total expected income:
- Sum up the expected policy income for all policies and all years.
5. Compare the total expected income to the cost of selling the policies:
- Add the administrative/sale cost per policy to the total expected income.
- Evaluate the profitability of the insurance policy by comparing the total income to the total cost.
6. Test and verify the program:
- Test the program with small numbers of random inputs and manually verify the results.
- Scale up the simulation to include all 100,000 policies and run the program multiple times to observe any differences in the results. If there are differences, analyze what might have caused them and consider the implications for your analysis.
By following this approach, you can use a Monte Carlo simulation to estimate the expected policy income and determine the potential profitability of the new insurance policy for the company.