Application of the Kelly Criterion to Ornstein-Uhlenbeck Processes

TL;DR

This paper extends the Kelly criterion to continuous-time models with Ornstein-Uhlenbeck processes, proving the existence of optimal strategies and providing formulas for optimal portfolios, with implications for financial markets.

Contribution

It introduces a general framework for applying the Kelly criterion to Ornstein-Uhlenbeck processes and derives explicit formulas for optimal investment strategies.

Findings

Existence of optimal strategies in continuous-time models proven.

Explicit formula for optimal portfolio under certain conditions.

Analysis of investment properties in multi-OU process settings.

Abstract

In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio for a set of price processes satisfying some simple conditions. Properties of the optimal investment strategy for assets governed by multiple Ornstein-Uhlenbeck processes are studied. The paper ends with a short discussion of the implications of these ideas for financial markets.