Markov Decision Process Trading Model

A Markov Decision Process (MDP) is not a trading strategy in itself — it is a problem formulation. It casts trading, execution, and portfolio management as a sequential decision problem: at each decision epoch the agent observes a state, chooses an action, receives a reward, and the environment moves to a new state according to a transition kernel. The defining commitment is the Markov property — the next state and reward depend only on the current state and action, not on the full episode history. Formally an MDP is the tuple (S, A, T, R, γ), and a policy maps states to actions. The whole construction exists to make one object well-defined: the value function, the expected discounted cumulative reward of following a policy from a state. The Hambly, Xu & Yang survey treats the MDP explicitly as “the setting for many of the commonly used RL approaches” in finance, spanning Optimal Execution, portfolio optimisation, Market Making, option pricing, and smart order routing.

Markov Decision Process Trading Model defines Optimal Execution Markov Decision Process Trading Model relates Reinforcement Learning Trading Policy Hambly Xu Yang 2023 supports Markov Decision Process Trading Model

The MDP is solved by dynamic programming. The optimal value function satisfies the Bellman optimality equation — V*(s) equals the best action’s immediate reward plus the discounted expected value of the successor state — and value iteration or policy iteration computes it by iterating the Bellman operator to convergence. This is the classical, model-based route: the transition kernel and reward must be known or estimated up front, after which the optimum is computed exactly. Nasir et al 2021 is a textbook instance — it builds an MDP for American-option trading, estimates transition probabilities as conditional distributions of option prices given price-affecting factors from statistical data, and solves it by value iteration to a policy that maximises accumulated return on Microsoft and Coca-Cola options. The classic Almgren Chriss 2000 optimal-execution model is the same shape: liquidate a fixed position over a finite horizon, with state = remaining inventory and time, action = trade quantity, and a mean-variance implementation-shortfall cost. Pedersen 2023 confirms the dynamic-programming solution of Almgren-Chriss “align[s] with the model intuition.”

Richard Bellman defines Markov Decision Process Trading Model Nasir et al 2021 proposes Markov Decision Process Trading Model Almgren Chriss 2000 part-of Optimal Execution Curse of Dimensionality opposes Markov Decision Process Trading Model

The crucial distinction this vault investigates is MDP framing versus its solution method. The MDP says what the problem is; it does not say how to solve it. When the transition kernel and reward are fully specified, dynamic programming solves the MDP exactly — but only for small problems. Pedersen 2023 reports bluntly that the dynamic-programming approach “is infeasible for large portfolios”: the state space grows combinatorially, the Curse of Dimensionality. When the model is unknown — the realistic case for live markets — the MDP is instead solved from sampled experience by Reinforcement Learning Trading Policy methods, which is why RL is the sibling note: RL is how MDPs are solved when transitions and rewards are unknown. The other Markov siblings sit alongside as state-modelling tools: Hidden Markov Model Regime Detection and Markov Regime-Switching Model supply latent-state estimates that can populate an MDP’s state vector, and a Markov Chain Trading Model is the degenerate MDP with no actions.

Reinforcement Learning Trading Policy supports Markov Decision Process Trading Model Reinforcement Learning Trading Policy relates Markov Decision Process Trading Model Hidden Markov Model Regime Detection part-of Markov Decision Process Trading Model Markov Regime-Switching Model relates Markov Decision Process Trading Model Markov Chain Trading Model part-of Markov Decision Process Trading Model

On evidence of profitability, the honest grade is alleged, leaning towards useful framework, unproven edge. Three failure modes recur across the sources and should temper any backtest claim. First, the Markov assumption is itself the weak point: Lalor Swishchuk 2025 title their paper “Non-Markov Market-Making” precisely because real limit-order-book dynamics show jumps and memory, so the memoryless state is a convenient fiction — a form of Partial Observability. Second, state-space and reward design are unprincipled choices: an MDP’s state vector and reward (PnL, utility, inventory penalty) are hand-picked, and a mis-specified reward is silently optimised against — see State-Space Design and Reward Specification Error. Third, backtest artefacts inflate results: Lalor Swishchuk 2025 show that omitting “adverse fills” produces “large phantom gains” and warn that “many models … have often been shown to over-inflate results,” echoing Overfitting in Quantitative Trading and Data-Snooping Bias. None of the four sources reports live-trading, transaction-cost-adjusted profitability; Nasir et al 2021 is an in-sample case study, Pedersen 2023 is a simulation against a known model, and Lalor Swishchuk 2025 tested 200 simulated out-of-sample episodes. Markov framing is genuinely valuable — it makes Regime Classification usable as state and gives execution problems a rigorous objective — but as of these sources the profitable, repeatable trading outcome after Transaction Costs and Slippage and Out-of-Sample Backtesting remains unsubstantiated.

Lalor Swishchuk 2025 contradicts Markov Decision Process Trading Model Non-Stationarity opposes Markov Decision Process Trading Model Partial Observability opposes Markov Decision Process Trading Model Reward Specification Error opposes Markov Decision Process Trading Model State-Space Design relates Markov Decision Process Trading Model Markov Decision Process Trading Model relates Regime Classification

Connections

• Hambly Xu Yang 2023 — proposes_model, 2021-2023, source: https://arxiv.org/abs/2112.04553
• Pedersen 2023 — tests_strategy, 2023, source: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4508553
• Lalor Swishchuk 2025 — tests_strategy, 2024-2025, source: https://arxiv.org/html/2410.14504v2
• Nasir et al 2021 — proposes_model, 2021, source: https://ideas.repec.org/a/kap/compec/v58y2021i2d10.1007_s10614-020-10030-4.html
• Almgren Chriss 2000 — proposes_model, 2000, source: 2000 foundational paper
• Richard Bellman — proposes_model, 1950s, source: https://arxiv.org/abs/2112.04553
• Optimal Execution — optimises_policy, source: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4508553
• Market Making — optimises_policy, source: https://arxiv.org/html/2410.14504v2
• Reinforcement Learning Trading Policy — optimises_policy, source: https://arxiv.org/abs/2112.04553
• Hidden Markov Model Regime Detection — detects_regime, source: https://arxiv.org/abs/2112.04553
• Markov Regime-Switching Model — detects_regime, source: https://arxiv.org/abs/2112.04553
• Markov Chain Trading Model — proposes_model, source: https://arxiv.org/abs/2112.04553
• Curse of Dimensionality — suffers_overfitting_risk, source: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4508553
• Non-Stationarity — suffers_overfitting_risk, source: https://arxiv.org/html/2410.14504v2
• Partial Observability — suffers_overfitting_risk, source: https://arxiv.org/html/2410.14504v2
• Reward Specification Error — suffers_overfitting_risk, source: https://arxiv.org/html/2410.14504v2
• State-Space Design — suffers_overfitting_risk, source: https://arxiv.org/html/2410.14504v2
• Limit Order Book — trades_market, source: https://arxiv.org/html/2410.14504v2
• US Equity Market — trades_market, source: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4508553
• Options Market — trades_market, source: https://ideas.repec.org/a/kap/compec/v58y2021i2d10.1007_s10614-020-10030-4.html
• Regime Classification — detects_regime, source: https://arxiv.org/abs/2112.04553
• Overfitting in Quantitative Trading — suffers_overfitting_risk, source: https://arxiv.org/html/2410.14504v2
• Data-Snooping Bias — suffers_overfitting_risk, source: https://arxiv.org/html/2410.14504v2
• Transaction Costs and Slippage — includes_costs, source: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4508553
• Out-of-Sample Backtesting — lacks_live_evidence, source: https://arxiv.org/html/2410.14504v2

Sources

• Recent Advances in Reinforcement Learning in Finance — Hambly, Xu & Yang (arXiv 2112.04553 / Mathematical Finance 2023)
• Revisiting Optimal Execution of Portfolio Transactions: A Dynamic Programming and Reinforcement Learning Approach — Pedersen (SSRN 2023)
• Deep Reinforcement Learning in Non-Markov Market-Making — Lalor & Swishchuk (arXiv 2410.14504 / Risks 2025)
• A Markov Decision Process Model for Optimal Trade of Options Using Statistical Data — Nasir, Khursheed, Ali & Mustafa (Computational Economics 2021)