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Optimal risk sharing for lambda value-at-risk

Part of: Applications Mathematical economics

Published online by Cambridge University Press:  29 July 2024

Zichao Xia  and
Taizhong Hu Open the ORCID record for Taizhong Hu [Opens in a new window]
Zichao Xia*
Affiliation:
University of Science and Technology of China
Taizhong Hu*
Affiliation:
University of Science and Technology of China
*
*Postal address: International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China.
*Postal address: International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China.
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Abstract

A new risk measure, the Lambda Value-at-Risk (VaR), was proposed from a theoretical point of view as a generalization of the ordinary VaR in the literature. Motivated by the recent developments in risk sharing problems for the VaR and other risk measures, we study the optimization of risk sharing for the Lambda VaR. Explicit formulas of the inf-convolution and sum-optimal allocations are obtained with respect to the left Lambda VaRs, the right Lambda VaRs, or a mixed collection of the left and right Lambda VaRs. The inf-convolution of Lambda VaRs constrained to comonotonic allocations is investigated. Explicit formula for worst-case Lambda VaRs under model uncertainty induced by likelihood ratios is also given.

Keywords

risk measureinf-convolutionrisk allocationoptimal allocationcomonotonicitymodel uncertainty

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 62P05: Applications to actuarial sciences and financial mathematics

Information

Type
Original Article
Information
Advances in Applied Probability , Volume 57 , Issue 1 , March 2025 , pp. 171 - 203
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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