A Convex Optimization Approach to Multiple Stopping: Pricing Chooser Caps and Swing Options

Abstract

In this current work, we generalize the recent Pathwise Optimization approach of Desai et al to Multiple stopping problems. The approach also minimizes the dual bound as in Desai et al to find the best approximation architecture for the Multiple stopping problem. Though, we establish the convexity of the dual operator, in this setting as well, we cannot directly take advantage of this property because of the computational issues that arise due to the combinatorial nature of the problem. Hence, we deviate from the pure martingale dual approach to marginal dual approach of Meinshausen and Hambly and solve each such optimal stopping problem in the framework of Desai et al. Though, this Pathwise Optimization approach as generalized to the Multiple stopping problem is computationally intensive, we highlight that it can produce superior dual and primal bounds in certain settings.