Dynamic Minimization of Worst Conditional Expectation of Shortfall

Abstract

In a complete financial market model, the shortfall‐risk minimization problem at the terminal date is treated for the seller of a derivative security F. The worst conditional expectation of the shortfall is adopted as the measure of this risk, ensuring that the minimized risk satisfies certain desirable properties as the dynamic measure of risk, as proposed by Cvitanić and Karatzas (1999) . The terminal value of the optimized portfolio is a binary functional dependent on F and the Radon‐Nikodym density of the equivalent local martingale measure. In particular, it is observed that there exists a positive number x* that is less than the replicating cost xF of F, and that the strategy minimizing the expectation of the shortfall is optimal if the hedger's capital is in the range [x*, xF].

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