A Dynamic Programming Approach for Value-at-Risk Markov Decision Processes in Continuous Spaces

This study is the first to prove the validity of dynamic programming equations for Value-at-Risk Markov Decision Processes (VaR MDPs) in continuous spaces, covering both finite-horizon and infinite-horizon scenarios. Previously, related dynamic programming equations had only been derived and verified in finite state and action spaces, leaving the continuous-space problem unresolved for a long time. This framework can be used to characterize optimal dynamic strategies for optimal execution problems with VaR objectives, solving an open problem in the field.