Adaptive Robust Trading Under Model Uncertainty

We propose a new methodology, called adaptive robust control, for solving a discrete-time Markovian control problem subject to Knightian uncertainty. We apply the general framework to an optimal investment problem where the... [ view full abstract ]

We propose a new methodology, called adaptive robust control, for solving a discrete-time Markovian control problem subject to Knightian uncertainty. We apply the general framework to an optimal investment problem where the uncertainty comes from the fact that the true law of the underlying model is only known to belong to a certain family of probabilities. We provide a learning algorithm that reduces the model uncertainty through progressive learning about the unknown system. One pillar in the proposed methodology is the recursive construction of the confidence sets for the unknown parameter, which allows to establish the corresponding Bellman equations.