Minimizing Risk Exposure When the Choice of a Risk Measure Is Ambiguous

Erick Delage () and Jonathan Yu-Meng Li ()
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Erick Delage: HEC Montréal, Montréal H3T 2A7, Canada
Jonathan Yu-Meng Li: Telfer School of Management, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Management Science, 2018, vol. 64, issue 1, 327-344

Abstract: 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.

Keywords: risk measure; robust optimization; conditional value at risk; preference ambiguity (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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