Quantile-based risk sharing with heterogeneous beliefs
成果类型：
Article
署名作者：
Embrechts, Paul; Liu, Haiyan; Mao, Tiantian; Wang, Ruodu
署名单位：
Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Geneva; Michigan State University; Michigan State University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Waterloo
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-018-1313-1
发表日期：
2020
页码：
319-347
关键词：
摘要：
We study risk sharing problems with quantile-based risk measures and heterogeneous beliefs, motivated by the use of internal models in finance and insurance. Explicit forms of Pareto-optimal allocations and competitive equilibria are obtained by solving various optimization problems. For Expected Shortfall (ES) agents, Pareto-optimal allocations are shown to be equivalent to equilibrium allocations, and the equilibrium pricing measure is unique. For Value-at-Risk (VaR) agents or mixed VaR and ES agents, a competitive equilibrium does not exist. Our results generalize existing ones on risk sharing problems with risk measures and belief homogeneity, and draw an interesting connection to early work on optimization properties of ES and VaR.