Paper: arXiv 2502.04284

Authors: Chutian Ma, Paul Smith

Abstract

We consider the multi-period portfolio optimization problem with a single asset that can be held long or short. Due to the presence of transaction costs, maximizing the immediate reward at each period may prove detrimental, as frequent trading results in consistent negative cash outflows. To simulate alpha decay, we consider a case where not only the present value of a signal, but also past values, have predictive power. We formulate the problem as an infinite horizon Markov Decision Process and seek to characterize the optimal policy that realizes the maximum average expected reward. We propose a variant of the standard value iteration algorithm for computing the optimal policy. Establishing convergence in our setting is nontrivial, and we provide a rigorous proof. Addtionally, we compute a first-order approximation and asymptotics of the optimal policy with small transaction costs.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous mathematical treatment of multi-period portfolio optimization under alpha decay and transaction costs, complete with Bellman equations and convergence proofs. However, it relies heavily on analytical formulations and toy numerical simulations rather than empirical validation against real-world market data.

Research Flowchart

  flowchart TD
    A[Goal: Optimal Multi-Period Trading Strategy<br/>with Alpha Decay & Transaction Costs] --> B[Inputs: Current & Past Signals Alpha Decay,<br/>Single Asset Long/Short, Transaction Cost Matrix]
    B --> C[Formulate Infinite Horizon<br/>Markov Decision Process MDP]
    C --> D[Develop Variant of<br/>Value Iteration Algorithm]
    D --> E[Prove Convergence & Compute<br/>First-Order Asymptotics Small Costs]
    E --> F[Outcome: Characterized Optimal Trading Policy<br/>Maximizing Average Expected Reward]

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1 of 31 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.