Chapter 4: Reinsurance (Equivalent CAS/SOA C/4 Section 29)

25 Oct

So far, I’ve had the inside track inasmuch as the topics were topics that were important to my earlier statistical studies. ‘Reinsurance’ however is not something that is required to be understood by all that many statisticians. (Apologies for pretending English is Latin, and trying to use the ablative absolute)

First, let us summarise the chapter:

We start with some terminology. Reinsurance is a method of risk transfer from one insurer to another. This chapter looks at three simple forms:

  1. Proportional reinsurance. Does what is says on the tin
  2. Excess of loss reinsurance. The insurer is responsible for paying the claim to a value M. Above M the reinsurer is responsible, until an excess limit reach, at which point the original insurer is again responsible
  3. Stop loss insurance. The reinsurers has the responsibility to pay the amount owing over a claim amount M with no upper limit.

We saw in the last chapter that given a set of claim data, it is relatively straight forward to model the size of claims – one can check various distributions for their goodness of fit. The meat of this chapter is how to convert the expressions for conditional probability from both the original insurer’s and the reinsurer’s point of view into tracatble algebraic expressions.

To provide the future actuary with the tools to apply these expressions, we are given  formulae for the moments of lognormal and normal, to simplify finding the moments of these distributions without needing to explicitly integrate the cdf, necessary we suppose due to the difficulty of integrating the Gaussian distribution.

There is also some salad in the form of discussions of the implications of inflation (if the size of claim is changed by inflation, but the retention limit is stationary, who does this effect the probability of exceeding the limit?), the difficulty in estimating the values of estimators if the data is censored by the retention limit e.g. claim amounts above the retention limit only show as the retention limit and a simple statement of fact that an excess paid by a consumer policyholder holding a general insurance is mathematically identical to the position of an insurer holding a reinsurance policy.

 

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