Large Deviations for a Class of Multivariate Heavy-Tailed Risk Processes Used in Insurance and Finance

Miriam Hägele and Jaakko Lehtomaa
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Miriam Hägele: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 64 (Gustaf Hällströmin katu 2), FI-00014 Helsinki, Finland
Jaakko Lehtomaa: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 64 (Gustaf Hällströmin katu 2), FI-00014 Helsinki, Finland

JRFM, 2021, vol. 14, issue 5, 1-18

Abstract: Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the main problems is to decide if there is any type of dependence between the components of the vector and, if so, what type of dependence structure should be used for accurate modelling. We study a class of heavy-tailed multivariate random vectors under a non-parametric shape constraint on the tail decay rate. This class contains, for instance, elliptical distributions whose tail is in the intermediate heavy-tailed regime, which includes Weibull and lognormal type tails. The study derives asymptotic approximations for tail events of random walks. Consequently, a full large deviations principle is obtained under, essentially, minimal assumptions. As an application, an optimisation method for a large class of Quota Share (QS) risk sharing schemes used in insurance and finance is obtained.

Keywords: large deviations; subexponential distribution; multivariate random walk; elliptical distribution (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2021
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