{"title":"Risk sharing under heterogeneous beliefs without convexity","authors":"Felix-Benedikt Liebrich","doi":"10.1007/s00780-024-00540-6","DOIUrl":null,"url":null,"abstract":"<p>We consider the problem of finding (Pareto-)optimal allocations of risk among finitely many agents. The associated individual risk measures are law-invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measures. Moreover, we assume that the individual risk assessments are consistent with the respective second-order stochastic dominance relations, but remain agnostic about their convexity. A simple sufficient condition for the existence of Pareto optima is provided. The proof combines local comonotonic improvement with a Dieudonné-type argument, which also establishes a link of the optimal allocation problem to the realm of “collapse to the mean” results.</p>","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"46 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finance and Stochastics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00780-024-00540-6","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the problem of finding (Pareto-)optimal allocations of risk among finitely many agents. The associated individual risk measures are law-invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measures. Moreover, we assume that the individual risk assessments are consistent with the respective second-order stochastic dominance relations, but remain agnostic about their convexity. A simple sufficient condition for the existence of Pareto optima is provided. The proof combines local comonotonic improvement with a Dieudonné-type argument, which also establishes a link of the optimal allocation problem to the realm of “collapse to the mean” results.
期刊介绍：
The purpose of Finance and Stochastics is to provide a high standard publication forum for research
- in all areas of finance based on stochastic methods
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Finance and Stochastics encompasses - but is not limited to - the following fields:
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- portfolio selection
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- term structure models
- statistical and empirical financial studies based on advanced stochastic methods
- numerical and stochastic solution techniques for problems in finance
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