Abstracts

We study the optimal investment problem with portfolio constraints and nonlinear trading costs where we optimize over adapted left continuous processes of bounded variation. We apply the conjugate duality framework to the problem so that the parameters enter the problem as pairs of random variables and optional random measures that describe the amount of cash to be delivered at the terminal time and the quantities of assets to be delivered over time. We derive a dual representation for the optimal value function and we give conditions for the existence of solutions. In particular, for markets with proportional transaction costs without portfolio constraints, we recover well-known dual expressions in terms of consistent price systems.