Non-convex dynamic programming and optimal investment

Teemu Penannen, Ari-Pekka Perkkiö, Miklós Rásonyi

Published 2015-04-08Version 1

We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal portfolios for non-concave utility maximization problems in financial market models with frictions (such as illiquidity), a first result of its kind. The proofs are based on the dynamic programming principle whose validity is established under quite general assumptions.