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Optimal Multiple Stopping of Linear Diffusions

Department of Operations Research and Financial Engineering, and the Bendheim Center for Finance, Princeton University, Princeton, New Jersey 08544
Department of Operations Research and Financial Engineering, and the Bendheim Center for Finance, Princeton University, Princeton, New Jersey 08544
rcarmona{at}princeton.edu
sdayanik{at}princeton.edu

Motivated by the analysis of financial instruments with multiple exercise rights of American type and mean reverting underlyers, we formulate and solve the optimal multiple-stopping problem for a general linear regular diffusion process and a general reward function. Instead of relying on specific properties of geometric Brownian motion and call and put option payoffs as in most of the existing literature, we use general theory of optimal stopping for diffusions, and we illustrate the resulting optimal exercise policies by concrete examples and constructive recipes.

Key Words: optimal multiple stopping; Snell envelope; diffusions; swing options
History: Received: November 23, 2006; revision received: September 12, 2007;