Portfolio construction with Gaussian mixture returns and exponential utility via convex optimization

We consider the problem of choosing an optimal portfolio, assuming the asset returns have a Gaussian mixture 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.