Your company offers personal illness insurance, which has 100 policyholders in the current policy year (2022). The insurance policy provides annual benefit payments to the policyholders if they have sickness during the year. The payment varies with 2 levels of sickness: mild sickness and severe sickness. The premium and sickness benefits are as follows: Annual premium of $200 is paid by a healthy policyholder who does not have sickness in the year. The annual payment for people with mild sickness in the year is $600. The annual payment for people with severe sickness in the year is $1000. A discrete-time Markov chain is used to model the portfolio. You can assume that: For policyholders without sickness, 10% will have mild sickness and 5% will have severe sickness in the next year. For people with mild sickness, 30% will have severe sickness and 50% will be healthy without sickness in the next year. For people with severe sickness, 40% will have mild sickness and 20% will be healthy without sickness in the next year. You are given the dataset for the 100 policyholders (file policydata.csv ). This dataset contains the status of policyholders in 2022.

Answer the following questions: Perform 1,000 simulations and provide the distribution of policyholders in 2024 and 2026 (that is, what is the % or the number of policyholders who will pay the premium or receive each type of sickness payment).

Explain the steps you have taken to obtain the answer.

Calculate the expected profit in 2024 and 2026 for your company.