Quantile-Based Risk Sharing

• 成果类型: Article
• 署名作者: Embrechts, Paul; Liu, Haiyan; Wang, Ruodu
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI); Michigan State University; Michigan State University; University of Waterloo
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1716
• 发表日期: 2018
• 页码: 936-949
• 关键词: law-invariant; expected-utility; Systemic risk; qualitative robustness; Regulatory arbitrage; optimal reinsurance; model uncertainty; coherent measures; equilibria; ORDER

摘要

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called range-value-at-risk (RVaR), as their preferences. The family of RVaR includes the value-at-risk (VaR) and the expected shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first establish an inequality for RVaR-based risk aggregation, showing that RVaR satisfies a special form of subadditivity. Then, the Pareto-optimal risk sharing problem is solved through explicit construction. To study risk sharing in a competitive market, an Arrow-Debreu equilibrium is established for some simple yet natural settings. Furthermore, we investigate the problem of model uncertainty in risk sharing and show that, in general, a robust optimal allocation exists if and only if none of the underlying risk measures is a VaR. Practical implications of our main results for risk management and policy makers are discussed, and several novel advantages of ES over VaR from the perspective of a regulator are thereby revealed.