Conditional value-at-risk in the presence of multiple probability measures

Craig Friedman

Abstract

ABSTRACT

Despite the widespread realization that risk measures depend critically on the underlying probability measure, most risk measures are based on single probability measures – asset price probabilities are assumed to be known with certainty. We explore practical methods to specify and compute the conditional value-at-risk, a coherent risk measure, in the presence of certain tractable collections of probability measures (risk measurement). Our methods “discover” the most dangerous measure in the set of measures. We also explore practical methods to compute optimal trading strategies with respect to a particular probability measure, under the constraint that CVAR is bounded under multiple probability measures (risk management).