When Inflation Causes No Increase in Claim Amounts

It is well known that when (re)insurance coverages involve a deductible, theimpact of inflation of loss amounts is distorted, and the changes in claims paid by the(re)insurer cannot be assumed to reflect the rate of inflation. A particularly interestingphenomenon occurs when losses follow a Pareto distribution. In this case, the observed lossamounts (those that exceed the deductible) are identically distributed from year to yeareven in the presence of inflation. Nevertheless, in this paper we succeed in estimating theinflation rate from the observations. We develop appropriate statistical inferential methodsto quantify the inflation rate and illustrate them using simulated data. Our solution hingeson the recognition that the distribution of the number of observed losses changes from yearto year depending on the inflation rate