Paper: arXiv 2407.15105

Authors: Hasanjan Sayit

Abstract

We prove that weak convergence within generalized gamma convolution (GGC) distributions implies convergence in the mean value. We use this fact to show the robustness of the expected utility maximizing optimal portfolio under exponential utility function when return vectors are modelled by hyperbolic distributions.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides rigorous mathematical proofs regarding the convergence properties of Generalized Gamma Convolution (GGC) distributions and applies them to exponential utility optimization. However, it is entirely theoretical with no empirical backtests, historical data analysis, or numerical simulations included in the text.

Research Flowchart

  flowchart TD
    A[Research Goal: Prove weak convergence implies<br/>mean convergence in GGC & assess portfolio robustness] --> B[Theoretical Proof: Analyze weak convergence<br/>properties in GGC distributions]
    B --> C[Key Theoretical Outcome: Weak convergence<br/>implies convergence in mean within GGC]
    D[Inputs: Equities return vectors modelled by<br/>Hyperbolic Distributions & Exponential Utility] --> E[Applied Analysis: Evaluate expected utility<br/>maximizing optimal portfolio]
    C --> E
    E --> F[Key Outcome: Demonstrated robustness of optimal<br/>portfolio under hyperbolic distribution assumptions]

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