Non-convex dynamic programming and optimal investment

TL;DR

This paper proves the existence of optimal investment strategies in complex financial models with non-convex utilities and market frictions, using a general dynamic programming approach without convexity assumptions.

Contribution

It introduces a novel existence proof for optimal portfolios in non-concave utility maximization problems under broad market conditions.

Findings

Existence of minimizers in non-convex stochastic optimization.

Optimal portfolios exist in markets with frictions like illiquidity.

Dynamic programming principle holds under general assumptions.

Abstract

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.