2025/11/03 by Gusti van Zyl, van Zyl, Gusti
Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Risk and Portfolio Optimization #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.2511.01540
We study distributionally robust Expected Shortfall when the distribution of the underlying is perturbed by a size quantified with optimal transport distance based on the quadratic cost function. In the dual version of the robust expectation problem, which is part of the robest expected shortfall problem, the computation of the so-called λc-transform fλc of payoff f is required. We show that under the quadratic cost function there exists a tractable representation of fλc, if f is convex. Furthermore, we show that robust expected shortfall can be characterized as the solution of a 2-dimensional minimization problem. We apply these results to obtain a closed-form formula for robust, with respect to the risk-neutral distribution, Expected Shortfall of an unhedged call option, from the point of view of the writer.