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Optimal multiple stopping of linear diffusions. (English) Zbl 1221.60061
Summary: 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 motions and call and put option payoffs as in most of the existing literature, we use the general theory of optimal stopping for diffusions, and illustrate the resulting optimal exercise policies by concrete examples and constructive recipes.

MSC:
60G40 Stopping times; optimal stopping problems; gambling theory
60J60 Diffusion processes
91G20 Derivative securities (option pricing, hedging, etc.)
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