Minimizing Risk Exposure When the Choice of a Risk Measure Is Ambiguous
研究了在决策者风险态度不确定时，如何利用已知的偏好信息（如风险度量应满足的性质和成对比较）来寻找最坏情况下的最优金融头寸，并给出了数值求解方法。
Since the financial crisis of 2007–2009, there has been a renewed interest in quantifying more appropriately the risks involved in financial positions. Popular risk measures such as variance and value-at-risk have been found inadequate because we now give more importance to properties such as monotonicity, convexity, translation invariance, positive homogeneity, and law invariance. Unfortunately, the challenge remains that it is unclear how to choose a risk measure that faithfully represents a decision maker’s true risk attitude. In this work, we show that one can account precisely for (neither more nor less than) what we know of the risk preferences of an investor/policy maker when comparing and optimizing financial positions. We assume that the decision maker can commit to a subset of the above properties (the use of a law invariant convex risk measure for example) and that he can provide a series of assessments comparing pairs of potential risky payoffs. Given this information, we propose to seek financial positions that perform best with respect to the most pessimistic estimation of the level of risk potentially perceived by the decision maker. We present how this preference robust risk minimization problem can be solved numerically by formulating convex optimization problems of reasonable size. Numerical experiments on a portfolio selection problem, where the problem reduces to a linear program, will illustrate the advantages of accounting for the fact that the choice of a risk measure is ambiguous. This paper was accepted by Yinyu Ye, optimization.