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Tail risk driven by investment losses and exogenous shocks

Published online by Cambridge University Press:  10 October 2024

Xinyue Man Open the ORCID record for Xinyue Man [Opens in a new window]  and
Qihe Tang Open the ORCID record for Qihe Tang [Opens in a new window]
Xinyue Man*
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China School of Risk and Actuarial Studies, UNSW Business School, UNSW Sydney, Sydney, NSW 2052, Australia
Qihe Tang
Affiliation:
School of Risk and Actuarial Studies, UNSW Business School, UNSW Sydney, Sydney, NSW 2052, Australia
*
Corresponding author: Xinyue Man; Email: [email protected]
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Abstract

Consider a company whose business carries the potential for investment losses and is additionally vulnerable to exogenous shocks. The unpredictability of the shocks makes it challenging for both the company and the regulator to accurately assess their impact, potentially leading to an underestimation of solvency capital when employing traditional approaches. In this paper, we utilize a stylized model to conduct an extreme value analysis of the tail risk of the company under a Fréchet-type and a Gumbel-type shock. Our main results explicitly demonstrate the different roles of investment risk and shock risk in driving large losses. Furthermore, we derive asymptotic estimates for the value at risk and expected shortfall of the total loss. Numerical studies are conducted to examine the accuracy of the obtained estimates.

Keywords

Tail riskshockregular variationmax-domain of attractionuniformity
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 54 , Issue 3 , September 2024 , pp. 712 - 737
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The International Actuarial Association

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