Write up guide part B.

The general structure of your report should be as follows: the inputs for your calculation (statistics), the method and code you used to derive your answer (you should copy and paste the code you use in your write up) and try to discuss how it works, the results from your model or calculation, trying to interpret your results. You SHOULD NOT paste 10000s of simulated values into your write up.

Breaking this down into the sections:

Question 2A and 2B, discuss the idea of the Empirical CDF and then discuss how you fit the Pareto and Gamma distribution to the dataset. You need to copy and paste your Pareto and Gamma code into your write up and discuss how these functions work perhaps relating them to equations from the class. You need display the graphs and comment on which distribution you decide provides the best fit.

Question 2C,. you should discuss the frequency severity model and the idea of simulation or generating random variables from distributions. Discuss how you will use the Poisson distribution for the frequency and discuss how you calculate the average frequency for each group of policies. Discuss the idea of estimating the Aggregate loss from the sum of individual losses. You need to paste the code you use and try to explain how it works. Discuss how you can calculate the aggregate loss over both groups if they are independent.

Does the Central Limit Theorem suggest that the Aggregate Claims Distribution (gamma and Pareto) is Normal?

Question 2D: Discuss how you can estimate the aggregate loss distribution using the output from your simulation in 2C and produce a graph of the result. You need to discuss how you could estimate the PML from this or the probability of observing a loss greater than a given value.

Question 2E: Discuss how you can also use the simulation to estimate the distributions of profits, and again graph your results . Discuss how you calculate the probability of making a loss.

Question 2F: Discuss how you could use your Profit Distribution to calculate the SCR. Try to link this to your diagram of the profit distribution.

Question 3: Discuss how you can derive the mean and variance of the aggregate claim for group A and group B by simply using equations and statistics. You need to discuss why you should use the Theoretical Pareto Variance rather than the variance from the losses for Group A and relate this to the equations provided. You need to say how you can derive the mean and variance Aggregate Claim across both Group A and Group B, and the assumptions behind this. You need to say how you can derive the Mean and the variance of the underwriting profit. You should then discuss why it might be reasonable to assume that the distribution of profits might be Normal and how you could use this to make the required calculations, perhaps using graphs of the CDF if possible. Finally you should compare your answers using the Normal Approximation and your Monte Carlo Simulation and see if there is any difference, and if possible explain the reason for any difference or similarity in the results.

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