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Optimal risk sharing for lambda value-at-risk
Published online by Cambridge University Press: 29 July 2024
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
MSC classification
Primary:
91B30: Risk theory, insurance
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- Original Article
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- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust
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