Optimal variance stopping with linear diffusions |
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Institution: | 1. Section of Pediatric Intensive Care, Department of Pediatrics and Child Health, and University of Manitoba, Children''s Hospital, Winnipeg, Manitoba, Canada;2. Faculty of Health Disciplines, Athabasca University, Athabasca, Alberta, Canada |
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Abstract: | We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game theory by doing so. Our main result shows that an optimal solution can, in a general case, be found among stopping times that are mixtures of two hitting times. This and other revealed phenomena together with suggested solution methods could be helpful when facing more complex non-linear optimal stopping problems. The results are illustrated by a few examples. |
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Keywords: | Optimal stopping Variance Non-linear optimal stopping Linear diffusion Infinite zero-sum game |
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