CONSTRAINED OPTIMIZATION WITH RESPECT TO STOCHASTIC DOMINANCE: APPLICATION TO PORTFOLIO INSURANCE

We are concerned with a classic portfolio optimization problem where the admissible strategies must dominate a floor process on every intermediate date (American guarantee). We transform the problem into a martingale, whose aim is to dominate an obstacle, or equivalently its Snell envelope. The optimization is performed with respect to the concave stochastic ordering on the terminal value, so that we do not impose any explicit specification of the agent's utility function. A key tool is the representation of the supermartingale obstacle in terms of a running supremum process. This is illustrated within the paper by an explicit example based on the geometric Brownian motion.