Investment optimization under constraints

Abstract.

We extend the duality approach developed by Kramkov and Schachermayer (1999) to cover the case of a general financial framework that includes models with some “imperfection”, such as constrained proportion portfolios, labor income, random endowment and large investor. General objective functions such as deterministic or random utility functions and shortfall risk loss functions are considered. Under a minimal set of assumptions equivalent to the asymptotic elasticity condition imposed on the agent’s utility function, we present an optimal investment theorem and, at the same time, address the corresponding dual problem.