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MULTIVARIATE DISTRIBUTIONS WITH TIME AND CROSS-DEPENDENCE: AGGREGATION AND CAPITAL ALLOCATION

Published online by Cambridge University Press:  27 April 2022

Xiang Hu  and
Lianzeng Zhang
Xiang Hu*
Affiliation:
School of Finance Zhongnan University of Economics and Law Nanhu Road, Wuhan, 430073, P.R. China
Lianzeng Zhang
Affiliation:
Department of Actuarial Science, School of Finance Nankai University Tongyan Road, Tianjin, 300350, P.R. China E-mail: [email protected]
*
E-mail: [email protected]
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Abstract

This paper investigates risk aggregation and capital allocation problems for an insurance portfolio consisting of several lines of business. The class of multivariate INAR(1) processes is proposed to model different sources of dependence between the number of claims of the portfolio. The total capital required for the whole portfolio is evaluated under the TVaR risk measure, and the contribution of each line of business is derived under the TVaR-based allocation rule. We provide the risk aggregation and capital allocation formulas in the general case of continuous and strictly positive claim sizes and then in the case of mixed Erlang claim sizes. The impact of both time dependence and cross-dependence on the behavior of risk aggregation and capital allocation is numerically illustrated.

Keywords

Multivariate INAR(1) processestime dependencecross-dependencerisk aggregationcapital allocation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 2 , May 2022 , pp. 669 - 706
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The International Actuarial Association

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