On a Joint Frequency and Severity Loss Model Applied to Earthquake Risk

26 Pages Posted: 7 Sep 2017

See all articles by Mathieu Boudreault

Mathieu Boudreault

University of Quebec at Montreal (UQAM)

Hélène Cossette

Université Laval - Faculté des Sciences et Génie

Etienne Marceau

Université Laval - Faculté des Sciences et Génie

Date Written: August 9, 2017

Abstract

In the seismological and geophysics literature, it is suggested by numerous authors that the elapsed time between two earthquakes at a given location should be represented by either an exponential or Weibull distribution. In addition, the seismic gap hypothesis states that large waiting times could provoke larger earthquakes. This will create a statistical dependence relationship between the frequency and magnitude components of any earthquake risk model. This paper investigates the actuarial, statistical and risk management implications of these two characteristics of earthquake risk. To do so, we introduce the conditional Weibull renewal process to count the number of earthquakes over a given time period and we introduce statistical dependence between the interarrival times and the force of each earthquake. An actuarial earthquake risk model based on these elements is presented and applied to Montreal (Quebec) earthquake data.

Keywords: Earthquake Risk, Risk Management, Conditional Weibull Renewal Process, Seismic Gap Hypothesis

JEL Classification: C60, C63, C02, G22

Suggested Citation

Boudreault, Mathieu and Cossette, Hélène and Marceau, Etienne, On a Joint Frequency and Severity Loss Model Applied to Earthquake Risk (August 9, 2017). Available at SSRN: https://ssrn.com/abstract=3015906 or http://dx.doi.org/10.2139/ssrn.3015906

Mathieu Boudreault

University of Quebec at Montreal (UQAM) ( email )

PB 8888 Station DownTown
Succursale Centre Ville
Montreal, Quebec H3C3P8
Canada

Hélène Cossette

Université Laval - Faculté des Sciences et Génie ( email )

1033, Pavillon Alexandre-Vachon
Cite Universitaire, Quebec G1K 7P4
Canada
418-656-2603 (Phone)

Etienne Marceau (Contact Author)

Université Laval - Faculté des Sciences et Génie ( email )

1033, Pavillon Alexandre-Vachon
Cite Universitaire, Quebec G1K 7P4
Canada
418-656-2013 (Phone)

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