Paper: arXiv 2503.17927

Authors: Levon Hakobyan, Sergey Lototsky

Abstract

While the Kelly portfolio has many desirable properties, including optimal long-term growth rate, the resulting investment strategy is rather aggressive. In this paper, we suggest a unified approach to the risk assessment of the Kelly criterion in both discrete and continuous time by introducing and analyzing the asymptotic variance that describes fluctuations of the portfolio growth, and use the results to propose two new measures for quantifying risk.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework for analyzing the Kelly criterion using Central Limit Theorem fluctuations and asymptotic variance. However, it is primarily theoretical with minimal empirical testing or backtesting on real-world asset data provided in the excerpt.

Research Flowchart

  flowchart TD
    A[Research Goal: Assess & mitigate risk in Kelly Criterion portfolio growth] --> B[Inputs: Discrete & Continuous Time Financial Models]
    B --> C[Methodology: Derive Asymptotic Variance of Portfolio Growth]
    C --> D[Compute: Analyze Growth Rate Fluctuations & Tail Risks]
    D --> E[Outcome: 2 New Risk Quantifying Measures for Kelly Betting]
    D --> F[Outcome: Optimized Capital Allocation Balancing Growth & Volatility]

Cited References (36)

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  2. Shrinkage estimation of Kelly portfolios (2018) — link
  3. Some analysis of a stochastic logistic growth model (2018) — link
  4. Positive Harris recurrence of the CIR process and its applications (2013) — link
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  6. Markov Processes: Characterization and Convergence (2005)
  7. A Theory for the Term Structure of Interest Rates (2004) — link
  8. Performance Measurement in a Downside Risk Framework (1994) — link
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0 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.