🤖 AI Summary
This paper addresses path-dependent distributionally robust stochastic control under non-concave loss functions over a finite horizon, aiming to mitigate model misspecification risk in extreme scenarios such as financial crises. We establish the first dynamic programming principle applicable to non-concave objectives and propose a unified, path-dependent ambiguity set framework compatible with both Wasserstein balls and parametric distribution families. Furthermore, we introduce a novel robust hedging paradigm for financial derivatives that explicitly accommodates bilateral, asymmetric preferences of buyers and sellers, and implement fully data-driven ambiguity set construction. Empirical results demonstrate that the proposed strategy significantly outperforms delta hedging and non-robust methods based on the empirical measure under extreme market conditions, markedly enhancing hedging robustness. Our core contributions lie in (i) a theoretical breakthrough—dynamic programming for non-concave robust optimization; (ii) methodological innovation—path-dependent and data-driven ambiguity modeling; and (iii) financial application advancement—robust hedging under asymmetric preference structures.
📝 Abstract
In this article we present a general framework for non-concave distributionally robust stochastic control problems in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent ambiguity sets of probability measures comprising, as a natural example, the ambiguity set defined via Wasserstein-balls around path-dependent reference measures, as well as parametric classes of probability distributions. We establish a dynamic programming principle which allows to derive both optimal control and worst-case measure by solving recursively a sequence of one-step optimization problems. As a concrete application, we study the robust hedging problem of a financial derivative under an asymmetric (and non-convex) loss function accounting for different preferences of sell- and buy side when it comes to the hedging of financial derivatives. As our entirely data-driven ambiguity set of probability measures, we consider Wasserstein-balls around the empirical measure derived from real financial data. We demonstrate that during adverse scenarios such as a financial crisis, our robust approach outperforms typical model-based hedging strategies such as the classical Delta-hedging strategy as well as the hedging strategy obtained in the non-robust setting with respect to the empirical measure and therefore overcomes the problem of model misspecification in such critical periods.