Paper: arXiv 2508.18868

Authors: Fabrizio Lillo, Piero Mazzarisi, Ioanna-Yvonni Tsaknaki

Abstract

The Kelly criterion provides a general framework for optimizing the growth rate of an investment portfolio over time by maximizing the expected logarithmic utility of wealth. However, the optimality condition of the Kelly criterion is highly sensitive to accurate estimates of the probabilities and investment payoffs. Estimation risk can lead to greatly suboptimal portfolios. In a simple binomial model, we show that the introduction of a European option in the Kelly framework can be used to construct a class of growth optimal portfolios that are robust to estimation risk.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical extension of the Kelly criterion to include European options in a discrete-time binomial setting, complete with formal proofs and KKT conditions. However, it relies entirely on synthetic toy simulations without any empirical validation or historical market backtesting.

Research Flowchart

  flowchart TD
    A["Research Question: How to mitigate Kelly Investing Estimation Risk?"] --> B["Data/Inputs: Binomial Asset Model & Probability/Payoff Parameters"]
    B --> C["Methodology: Integrate European Options into Kelly Framework"]
    C --> D["Computational Process: Maximize Expected Logarithmic Utility of Wealth"]
    D --> E["Outcome: Robust Growth-Optimal Portfolios Resilient to Parameter Errors"]

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0 of 75 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.