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The construction of replication strategies for contingent claims in thepresence of risk and market friction is a key problem of financial engineering.In real markets, continuous replication, such as in the model of Black, Scholesand Merton (BSM), is not only unrealistic but it is also undesirable due tohigh transaction costs. A variety of methods have been proposed to balancebetween effective replication and losses in the incomplete market setting. Withthe rise of Artificial Intelligence (AI), AI-based hedgers have attractedconsiderable interest, where particular attention was given to Recurrent NeuralNetwork systems and variations of the $Q$-learning algorithm. From a practicalpoint of view, sufficient samples for training such an AI can only be obtainedfrom a simulator of the market environment. Yet if an agent was trained solelyon simulated data, the run-time performance will primarily reflect the accuracyof the simulation, which leads to the classical problem of model choice andcalibration. In this article, the hedging problem is viewed as an instance of arisk-averse contextual $k$-armed bandit problem, which is motivated by thesimplicity and sample-efficiency of the architecture. This allows for realisticonline model updates from real-world data. We find that the $k$-armed banditmodel naturally fits to the Profit and Loss formulation of hedging, providingfor a more accurate and sample efficient approach than $Q$-learning andreducing to the Black-Scholes model in the absence of transaction costs andrisks.

Hedging using reinforcement learning: Contextual $k$-Armed Bandit versus $Q$-learning