Risk Sharing with Lambda Value at Risk

• 成果类型: Article
• 署名作者: Liu, Peng
• 署名单位: University of Essex
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0246
• 发表日期: 2025
• 关键词: law-invariant; Allocations

摘要

In this paper, we study the risk-sharing problem among multiple agents using lambda value at risk (AVaR) as their preferences via the tool of inf-convolution, where AVaR is an extension of value at risk (VaR). We obtain explicit formulas of the infconvolution of multiple AVaR with monotone A and explicit forms of the corresponding optimal allocations, extending the results of the inf-convolution of VaR. It turns out that the inf-convolution of several AVaR is still a AVaR under some mild condition. Moreover, we investigate the inf-convolution of one AVaR and a general monotone risk measure without cash additivity, including AVaR, expected utility, and rank-dependent expected utility as special cases. The expression of the inf-convolution and the explicit forms of the optimal allocation are derived, leading to some partial solution of the risk-sharing problem with multiple AVaR for general A functions. Finally, we discuss the risk-sharing problem with AVaR+, another definition of lambda value at risk. We focus on the inf-convolution of AVaR+ and a risk measure that is consistent with the second-order stochastic dominance, deriving very different expression of the inf-convolution and the forms of the optimal allocations.