Investment optimization under constraints

We analyze general stochastic optimization financial problems under constraints in a general framework, which includes financial models with some “imperfection”, such as constrained portfolios, labor income, random endowment and large investor models. By using general optional decomposition under constraints in a multiplicative form, we first develop a dual formulation under minimal assumption modeled as in Pham and Mnif (2002) [Ph-M], Long (2002) [L02a]. We then are able to prove an existence and uniqueness of an optimal solution to primal and to the corresponding dual problem. An optimal investment to the original problem then can be found by convex duality, similarly to the case considered by Kramkov and Schachermayer (1999) [K-Sch].