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Excel Assignment 2 for Math 523

Due: Midnight, Sunday, 26 November 2023

Consider the following compound model for annual losses: The random number of losses N follows a Poisson(3) distribution, and the random severity of each loss X follows a Pareto(3, 2000) distribution. An insurance policy applies a deductible of 500 to each loss, followed by coinsurance of 0.60. Let S denote the aggregate claims paid in one year.

For each of the simulations, use the inverse cdf or inverse survival function of the random variable.

A. Simulate 100 values from S’s distribution by the following steps:

1. Simulate a value for N ∼ Poisson(3).

2. Simulate N losses X ∼ Pareto(3, 2000).

3. Apply the policy provisions to each simulated value of X to get YL.

4. Add the N values of YL to get S for one year.

5. Repeat steps 1-4 to get 100 values of S.

B. Simulate another 100 values from S’s distribution by the following steps:

1. Determine the distribution of the number of positive claim payments NP .

2. Determine the distribution of the size of the positive claims payments YP .

3. Simulate a value for NP .

4. Simulate NP claim payments YP .

5. Add the NP values of YP to get S for one year.

6. Repeat steps 3-6 to get 100 values of S.

C. Compare means and variances.

1. Compute ES and VarS by using the representation S = Y1L + Y2L + · · · YNL.

2. Compute ES and VarS by using the representation S = Y1P + Y2P + · · · YNPP .

3. Compute the sample mean and variance of the 100 simulated values of S from part A.

4. Compute the sample mean and variance of the 100 simulated values of S from part B.