Closed-Form Solutions for Worst-Case Law Invariant Risk Measures with Application to Robust Portfolio Optimization

• 成果类型: Article
• 署名作者: Li, Jonathan Yu-Meng
• 署名单位: University of Ottawa
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2018.1736
• 发表日期: 2018
• 页码: 1533-1541
• 关键词: representation; bounds

摘要

Worst-case risk measures provide a means of calculating the largest value of risk when only partial information of the underlying distribution is available. For popular risk measures such as value-at-risk (VaR) and conditional value-at-risk (CVaR) it is now known that their worst-case counterparts can be evaluated in closed form when only the first two moments are known. We show in this paper that closed-form solutions exist for a general class of law invariant coherent risk measures, which consist of spectral risk measures (and thus CVaR also) as special cases. Moreover, we provide worst-case distributions characterized in terms of risk spectrums, which can take any form of distribution bounded from below. As applications of the closed-form results, new formulas are derived for calculating the worst-case values of higher order risk measures and higher order semideviation, and new robust portfolio optimization models are provided.