Optimal Investment Based on Performance Measure and Stochastic Benchmark Under PI and Position Constraints

We consider the portfolio selection problem faced by a manager under the performance ratio with position and portfolio insurance (PI) constraints. By making use of a dual control method in an incomplete market setting, we find the unique pricing kernel in the presence of closed convex cone control constraints. Then, following the same arguments as in the complete market case, we derive the explicit form of the optimal investment strategy by combining the linearization method, the Lagrangian method, and the concavification technique.