Optimal insurance design with Lambda-Value-at-Risk

Tim J. Boonen, Yuyu Chen, Xia Han and Qiuqi Wang

European Journal of Operational Research, 2025, vol. 327, issue 1, 232-246

Abstract: This paper explores optimal insurance solutions based on the Lambda-Value-at-Risk (ΛVaR). Using the expected value premium principle, we first analyze a stop-loss indemnity and provide a closed-form expression for the deductible parameter. A necessary and sufficient condition for the existence of a positive and finite deductible is also established. We then generalize the stop-loss indemnity and show that, akin to the VaR model, a limited stop-loss indemnity remains optimal within the ΛVaR framework. Further, we examine the use of Λ′VaR as a premium principle and show that full or no insurance is optimal. We also identify that a limited loss indemnity is optimal when Λ′VaR is solely used to determine the risk-loading in the premium principle. Additionally, we investigate the impact of model uncertainty, particularly in scenarios where the loss distribution is unknown but lies within a specified uncertainty set. Our findings suggest that a limited stop-loss indemnity is optimal when the uncertainty set is defined using a likelihood ratio. Meanwhile, when only the first two moments of the loss distribution are available, we provide a closed-form expression for the optimal deductible in a stop-loss indemnity.

Keywords: Risk management; Optimal insurance; Lambda-Value-at-Risk; Model uncertainty; Stop-loss (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:327:y:2025:i:1:p:232-246

DOI: 10.1016/j.ejor.2025.04.038

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