When Inflation Causes No Increase in Claim Amounts

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 Paret...

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Main Authors: Vytaras Brazauskas, Bruce L. Jones, Ričardas Zitikis
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2009/943926
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author Vytaras Brazauskas
Bruce L. Jones
Ričardas Zitikis
author_facet Vytaras Brazauskas
Bruce L. Jones
Ričardas Zitikis
author_sort Vytaras Brazauskas
collection DOAJ
description 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.
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publishDate 2009-01-01
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series Journal of Probability and Statistics
spelling doaj-art-71a24421be7f4d018ef2a5ea5ab30ece2025-02-03T05:58:05ZengWileyJournal of Probability and Statistics1687-952X1687-95382009-01-01200910.1155/2009/943926943926When Inflation Causes No Increase in Claim AmountsVytaras Brazauskas0Bruce L. Jones1Ričardas Zitikis2Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USADepartment of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, N6A 5B7, CanadaDepartment of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, N6A 5B7, CanadaIt 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.http://dx.doi.org/10.1155/2009/943926
spellingShingle Vytaras Brazauskas
Bruce L. Jones
Ričardas Zitikis
When Inflation Causes No Increase in Claim Amounts
Journal of Probability and Statistics
title When Inflation Causes No Increase in Claim Amounts
title_full When Inflation Causes No Increase in Claim Amounts
title_fullStr When Inflation Causes No Increase in Claim Amounts
title_full_unstemmed When Inflation Causes No Increase in Claim Amounts
title_short When Inflation Causes No Increase in Claim Amounts
title_sort when inflation causes no increase in claim amounts
url http://dx.doi.org/10.1155/2009/943926
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