Multistage Investments With Recourse: a Single-Asset Case with Transaction Costs

We consider a financial decision problem involving dynamic investment decisions on a single risky instrument over multiple and discrete time periods. Investment returns are assumed stochastic and possibly dependent over time, and proportional transaction costs are considered in the model. In this setting, the investor¿s goal is to determine investment policies that maximize the net profit while maintaining the associated risk under control. We propose approximations of the ensuing stochastic multistage optimization problem that are based on affine recourse strategies and that lead to efficiently solvable second order cone or semidefinite programs.