Inflation Adjustment

In the real world, the total claims will increase over time due to inflation. It is crucial that the insurers and reinsurers have prepared for the increase.

Baseline Insurance Company

Suppose that due to inflation next year, a typical claim next year will have distribution .

If is that part of the claim handled by the insurer this year, then next year it will be defined by

The expected value of the total insurers’ claim can be derived from the following steps:

First, we need to derive the density function and distribution fucntion of

Then, the expectation of is given by

Let , then and , and the above expectation becomes

Let , then and , and the above can be rewritten as

where is the density function of .

In addition, we can use the distribution function to show the expectation of .

Since has been defined as the minimum of and , we can rewritten the express as . So, the expecations of the baseline insurance company and reinsurance company are given by

So we can calculate the expectation of as

Let , then , , then we have:

The component in the curly brackets is the expectation of the minimum of the claim amount and the limit (), which is the expectation of the baseline insurance company. Therefore, we have:

Reinsurance Company

For the reinsurance company, the inflation adjustment is straghtforward.

The inflation-adjusted expectation of reinsurance can be calculated as follows: