  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.
