Application of the Kelly Criterion to Prediction Markets

ArXiv ID: 2412.14144 “View on arXiv”

Authors: Unknown

Abstract

Betting markets are gaining in popularity. Mean beliefs generally differ from prices in prediction markets. Logarithmic utility is employed to study the risk and return adjustments to prices. Some consequences are described. A modified payout structure is proposed. A simple asset price model based on flipping biased coins is investigated. It is shown using the Kullback-Leibler divergence how the misjudgment of the bias and the miscalculation of the investment fraction influence the portfolio growth rate.

Keywords: Betting Markets, Logarithmic Utility, Kullback-Leibler Divergence, Asset Pricing Model, Portfolio Growth Rate

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper uses advanced mathematical tools like Kullback-Leibler divergence and logarithmic utility derivations, showing high theoretical density, but lacks any backtesting, real data, or implementation details, making it primarily a theoretical exercise.

  flowchart TD
    A["Research Goal: Apply Kelly Criterion to Prediction Markets"] --> B["Methodology: Logarithmic Utility & Asset Pricing Model"]
    B --> C["Input: Biased Coin Flipping Data / Market Prices"]
    C --> D["Process: Misjudged Bias &<br/>Miscalculated Investment Fraction"]
    D --> E["Compute: Portfolio Growth Rate &<br/>Kullback-Leibler Divergence"]
    E --> F["Key Findings: Risk/Return Adjustments &<br/>Modified Payout Structures"]