Markov Decision Processes under Model Uncertainty
This work addresses portfolio optimization for investors by providing a robust framework to handle model uncertainty, though it is incremental as it builds on existing robust optimization methods.
The paper tackles robust portfolio optimization under model uncertainty by introducing a dynamic programming framework that solves a local robust optimization problem to obtain a global optimizer and worst-case measure. Applying the framework to S&P 500 data, it shows that robust strategies outperform non-robust ones in volatile or bearish market scenarios, with concrete performance gains implied.
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.