Journal of Probability and Statistics
Volume 2009 (2009), Article ID 943926, 10 pages
Research Article

When Inflation Causes No Increase in Claim Amounts

1Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA
2Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, N6A 5B7, Canada

Received 27 January 2009; Accepted 26 June 2009

Academic Editor: Tomasz J. Kozubowski

Copyright © 2009 Vytaras Brazauskas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is well known that when (re)insurance coverages involve a deductible, the impact 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 interesting phenomenon occurs when losses follow a Pareto distribution. In this case, the observed loss amounts (those that exceed the deductible) are identically distributed from year to year even in the presence of inflation. Nevertheless, in this paper we succeed in estimating the inflation rate from the observations. We develop appropriate statistical inferential methods to quantify the inflation rate and illustrate them using simulated data. Our solution hinges on the recognition that the distribution of the number of observed losses changes from year to year depending on the inflation rate.