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

arXiv: https://arxiv.org/abs/2205.04563 · HTML: https://mlsanity.com/paper/2205.04563/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2022.

## Built on by (most cited first, 4 of 4)

- [Distribution Transformers: Fast Approximate Bayesian Inference With On-The-Fly Prior Adaptation](https://mlsanity.com/paper/2502.02463/) (2025)
- [ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming](https://mlsanity.com/paper/2505.05261/) (2025)
- [Variational Bayes Portfolio Construction](https://mlsanity.com/paper/2411.06192/) (2024)
- [Generation of Custom Solvers in Rust for Convex Optimization](https://mlsanity.com/paper/2609.13875/) (2026)

## Abstract (arXiv)

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.