Markov Decision Processes

A Markov Decision Process provides a mathematical framework for modeling decision-making in situations where outcomes are partly random and partly under the control of a decision-maker. It consists of states, actions, transition probabilities, and rewards, forming the foundation for reinforcement learning in trading.

In the context of derivatives, a state might represent current portfolio Greeks and market conditions, while an action is the decision to hedge or hold. The goal is to find a policy that maximizes the expected return over time, accounting for the sequential nature of trading decisions.

This framework is essential for managing the long-term impact of current hedging actions on future portfolio stability.