A Convex Optimization Approach to Multiple Stopping

Authors: Shyam S Chandramouli

In this current work, we generalize the recent Pathwise Optimization approach of Desai et al.~\cite{desai2010pathwise} to Multiple stopping problems. The approach also minimizes the dual bound as in Desai et al.~\cite{desai2010pathwise} 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 \emph{marginal} dual approach of Meinshausen and Hambly~\cite{meinshausenhambly2004} and solve each such optimal stopping problem in the framework of Desai et al.~\cite{desai2010pathwise}. 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.

Comments: 22 Pages.

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Submission history

[v1] 2012-11-21 10:29:40

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