Stock Market Trading Via Stochastic Network Optimization

TL;DR

This paper introduces a stochastic network optimization-based trading policy for stock markets that adapts to random price fluctuations, achieving near-optimal profits under constraints, with proven performance for both ergodic and non-ergodic price processes.

Contribution

It develops a novel trading algorithm based on Lyapunov Optimization that approaches optimal profit under realistic market constraints and extends to non-ergodic price models.

Findings

Achieves near-optimal profit with bounded stock levels.

Works under ergodic and non-ergodic price assumptions.

Provides tradeoffs between profit proximity, stock levels, and convergence time.

Abstract

We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that prices evolve according to an ergodic process with a mild decaying memory property, and assuming constraints on the total number of shares that can be bought and sold at any time, we develop a trading policy that comes arbitrarily close to achieving the profit of an ideal policy that has perfect knowledge of future events. Proximity to the optimal profit comes with a corresponding tradeoff in the maximum required stock level and in the timescales associated with convergence. We then consider arbitrary (possibly non-ergodic) price processes, and show that the same algorithm comes close to the profit of a frame based policy that can look a fixed number of slots into the future. Our analysis uses techniques of Lyapunov Optimization that we originally developed for stochastic network optimization problems.