Portfolio Construction with Gaussian Mixture Returns and Exponential Utility via Convex Optimization

TL;DR

This paper presents a convex optimization approach for optimal portfolio construction assuming Gaussian mixture returns, maximizing exponential utility and minimizing entropic value at risk without sampling.

Contribution

It introduces a convex formulation for portfolio optimization with Gaussian mixture returns and exponential utility, enabling exact solutions without scenario sampling.

Findings

Convexity of the portfolio optimization problem with Gaussian mixture returns.

Exact solutions obtained using domain-specific convex optimization languages.

Formulation of entropic value at risk minimization as a convex problem.

Abstract

We consider the problem of choosing an optimal portfolio, assuming the asset returns have a Gaussian mixture (GM) distribution, with the objective of maximizing expected exponential utility. In this paper we show that this problem is convex, and readily solved exactly using domain-specific languages for convex optimization, without the need for sampling or scenarios. We then show how the closely related problem of minimizing entropic value at risk can also be formulated as a convex optimization problem.