Optimal decision under ambiguity for diffusion processes |
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Authors: | Sören Christensen |
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Institution: | 1. Christian-Albrechts-Universit?t, Ludewig-Meyn-Str. 4, 24098, Kiel, Germany
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Abstract: | In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary optimal stopping problems for one-dimensional Brownian motions we reduce the problem to the geometric problem of finding the smallest majorant of the reward function in a two-parameter function space. In a second part we solve optimal stopping problems when the underlying process may crash down. These problems are reduced to one optimal stopping problem and one Dynkin game. Examples are discussed. |
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