尾方差分配、Shapley值和优化问题

IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
M. Galeotti, Giovanni Rabitti
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引用次数: 0

摘要

Colini Baldeschi等人(2018)重点关注依赖风险组合中的风险贡献,引入了方差和标准差博弈的Shapley值。在这个注释中,我们扩展了他们的结果,引入了尾部方差以及尾部标准差对策。我们推导了尾方差对策的Shapley值的闭合形式表达式,并分析了这两个对策的向量优化问题。特别是,我们构造了两个例子,表明这两个游戏的风险贡献排名可能会根据条件阈值和尾部肥胖程度而颠倒。受这些例子的启发,我们提出了一个关于一般投资组合的猜想。最后,我们讨论了风险管理的含义,包括尾部协方差保费的特征和对等保单的再保险定价。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tail variance allocation, Shapley value, and the majorization problem
With a focus on the risk contribution in a portofolio of dependent risks, Colini-Baldeschi et al. (2018) introduced Shapley values for variance and standard deviation games. In this note we extend their results, introducing tail variance as well as tail standard deviation games. We derive closed-form expressions for the Shapley values for the tail variance game and we analyze the vector majorization problem for the two games. In particular, we construct two examples showing that the risk contribution rankings for the two games may be inverted depending on the conditioning threshold and the tail fatness. Motivated by these examples, we formulate a conjecture for general portfolios. Lastly, we discuss risk management implications, including the characterization of tail covariance premiums and reinsurance pricing for peer-to-peer insurance policies.
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来源期刊
Journal of Applied Probability
Journal of Applied Probability 数学-统计学与概率论
CiteScore
1.50
自引率
10.00%
发文量
92
审稿时长
6-12 weeks
期刊介绍: Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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