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

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Hägele , M & Lehtomaa , J 2021 , ' Large Deviations for a Class of Multivariate Heavy-Tailed Risk Processes Used in Insurance and Finance ' , Journal of risk and financial management , vol. 14 , no. 5 , 202 . https://doi.org/10.3390/jrfm14050202

Title: Large Deviations for a Class of Multivariate Heavy-Tailed Risk Processes Used in Insurance and Finance
Author: Hägele, Miriam; Lehtomaa, Jaakko
Contributor organization: Department of Mathematics and Statistics
Date: 2021-05-02
Language: eng
Number of pages: 18
Belongs to series: Journal of risk and financial management
ISSN: 1911-8066
DOI: https://doi.org/10.3390/jrfm14050202
URI: http://hdl.handle.net/10138/330618
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.
Subject: large deviations
subexponential distribution
multivariate random walk
elliptical distribution
RANDOM-WALKS
VOLATILITY
111 Mathematics
Peer reviewed: Yes
Rights: cc_by
Usage restriction: openAccess
Self-archived version: publishedVersion


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