Weak convergence implies convergence in mean within GGC

TL;DR

This paper demonstrates that within GGC distributions, weak convergence guarantees convergence in mean, and applies this to show the stability of utility-maximizing portfolios under hyperbolic return models.

Contribution

It establishes that weak convergence implies mean convergence in GGC distributions and applies this to portfolio optimization robustness.

Findings

Weak convergence implies convergence in mean for GGC distributions.

Expected utility maximization remains stable under hyperbolic return models.

The result enhances understanding of convergence properties in probabilistic models.

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.