ACTL5103: Stochastic Modelling for Actuaries - Accounting Assignment Help

Assignment Task :

1 Background 

You are an actuarial analyst at Skippie Insurance. Your company offers a Bonus-Malus System (BMS) car insurance scheme with 10,000 policyholders in the current policy year. 5,000 policyholders are males aged 20 to 25, and the remaining 5,000 are males aged 50 to 55. The base premium charged to policyholders is $300 per annum for males aged 50-55 and $400 per annum for males aged 20-25. For simplicity, you are to assume that the individual claim cost is $1,000 for both groups. Details of the current scheme (which applies to both groups of policyholders) is as follows:

Three tasks 

You have been asked by your manager to perform analyses on the current scheme. In particular, you have been asked to do the following: 

  Task 1: 

1. Determine the probability transition matrices for the three different schemes, for each group of policyholder. Your manager wants you to assume that the number of claims per year follows Poisson distribution with parameters λold = 0.15 and λyoung = 0.25. 2. For the current scheme only (see Table 1), simulate the number of policyholders in each of the discount levels for the year of 2021 (i.e. next year), 1000 times. Describe the distribution of next year's gross premium (provide summary statistics). 

  Task 2: 

1. Plot the Loimaranta efficiency of the three different schemes as a function of λ, the claim frequency and explain your results.

2. Compare the long-run profitability.

3. Recommend which system should be used and discuss the pros and cons of your choice (justification does not need to be limited to the above findings). 

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