Monte Carlo Simulation: Steps

Question 1

Steps

Answer 1

1. Collect data- must be credible
2. project the claims numbers data to ultimate to allow for events which have happened but have not yet been reported, ie IBNR claims.
3. Project claim amounts data will to ultimate to reflect
4. Adjust the data so that it is appropriate for the period of interest, eg to allow for changes in the:
   - mix of business
   - policy terms and conditions, eg limits and deductibles claims handling processes and reserving philosophy claims inflation
   - external claims environment, eg changes in the propensity to claim or legal rulings.
5. Fit the distribution using Poisson and gamma distributions eg by using the method of moments or maximum likelihood estimation.
6. The Monte Carlo simulation process would then work as follows:
   - Simulate the number of claims, n, from the fitted Poisson distribution
   - for each simulation of n, generate claim sizes x1, x2, at random from gamma distribution for ground up claims.
   - apply the policy terms and conditions to each xi, eg limits and deductibles
   - sum the resulting claim amounts together
   - apply further terms and conditions as appropriate, eg aggregate deductibles
   - repeat this process a large number of times (eg 10,000) to reach satisfactory convergence.

Question 2

Determine Price for different excesses using Montecarlo

Answer 2

Firstly the actuary should calculate the premium based on an excess of €5,000 as follows:
1.generate a number of claims from the fitted frequency distribution
2.for each claim, separately generate a corresponding claim amount from the fitted severity distribution
deduct the €5,000 excess, restricting the result to a minimum of zero
3. sum the resulting amounts to get an estimate of the risk premium.
4. This process should be repeated a large number of times to derive an average risk premium to charge with an excess of €5,000.
6. Allowance would then be made for loadings, such as expenses, tax, investment income etc.
7. Repeat with an excess of €10,000
8. compare to determine the theoretical difference in premium between the two excess level

Question 3

Treating Large Losses in experience

Answer 3

• Decide whether the large loss should be included to the data and perform analysis.
• If it is excluded allow for separately it as follows.
  a) Cap it then truncate it and spread any cost above this level across the larger portfolio of risks covered by the insurer. An assumption about the expected frequency of such large losses will be required.

b) Ignore the large loss altogether, eg if a change in policy conditions or legislation means that a claim of the same type could not occur in Year 6, or is at least highly improbable.