Bayesian Kelly Criterion with Parameter Uncertainty

Abstract

The classical Kelly criterion provides an optimal solution for position sizing by maximizing the expected logarithmic growth rate of capital. However, its practical application is severely limited by parameter uncertainty — practitioners rarely know the true probability of success p and must estimate it from finite samples. This paper develops a rigorous Bayesian framework for the Kelly criterion that explicitly accounts for estimation risk in the win probability. We derive closed-form solutions for optimal fractional Kelly sizing under beta-distributed probability beliefs, demonstrate the relationship between statistical confidence and position size reduction, and present a dynamic capital allocation system that adapts to changing uncertainty regimes. Monte Carlo simulations across varying sample sizes show that Bayesian Kelly substantially outperforms both full Kelly and ad-hoc fractional Kelly approaches, reducing maximum drawdown by 40–60% while maintaining 85–95% of optimal growth rates in realistic trading scenarios.

Keywords

• Kelly criterion
• Bayesian estimation
• Position sizing
• Estimation risk
• Fractional Kelly

Cite this paper

Sukhov, S. (2026). Bayesian Kelly Criterion with Parameter Uncertainty: A Robust Framework for Position Sizing Under Estimation Risk. MMRL Working Paper WP-2026-001. SSRN. https://doi.org/10.2139/ssrn.6195358

@techreport{sukhov2026bayesian,
  author      = {Sukhov, Sergei},
  title       = {Bayesian Kelly Criterion with Parameter Uncertainty: A Robust Framework for Position Sizing Under Estimation Risk},
  institution = {Market Microstructure Research Lab},
  type        = {MMRL Working Paper},
  number      = {WP-2026-001},
  year        = {2026},
  month       = mar,
  doi         = {10.2139/ssrn.6195358},
  url         = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6195358},
}

Research area

Drawdown-Constrained Capital Allocation