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Portfolio Optimization for Binary Options Based on Relative Entropy.

Peter Joseph Mercurio1, Yuehua Wu1, Hong Xie2

  • 1Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

We introduce discrete entropic portfolio optimization (DEPO), a new method for optimizing discrete return assets like binary options. DEPO outperforms the Kelly criterion in financial and gambling applications.

Keywords:
Kelly criterionKullback–Leibler divergencebinary optionsdigital optionsexotic optionsfixed-return optionsportfolio optimizationportfolio selectionrelative entropysports betting

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Area of Science:

  • Quantitative Finance
  • Computational Finance
  • Decision Theory

Background:

  • Traditional portfolio optimization assumes continuous returns.
  • Existing methods like REPO are effective for continuous returns but not discrete ones.
  • Discrete returns, common in binary options and gambling, require specialized optimization.

Purpose of the Study:

  • Extend the return-entropy portfolio optimization (REPO) to discrete return assets.
  • Introduce discrete entropic portfolio optimization (DEPO) for assets with discrete probability distributions.
  • Demonstrate DEPO's effectiveness in financial and gambling contexts.

Main Methods:

  • Formulated discrete entropic portfolio optimization (DEPO) based on expected growth rate and relative entropy.
  • Applied DEPO to portfolios of binary options (e.g., foreign exchange on NADEX).
  • Applied DEPO to portfolios of sports bets (e.g., NFL season).

Main Results:

  • DEPO provides an optimal strategy for discrete return assets.
  • DEPO outperformed leading Kelly criterion strategies in binary option trading.
  • DEPO demonstrated advantages over Kelly criterion strategies in sports betting.

Conclusions:

  • DEPO is a novel and effective optimization method for discrete return assets.
  • DEPO offers a superior alternative to the Kelly criterion for specific applications.
  • The framework is applicable to various discrete return scenarios, including finance and gambling.