Optimal decision under ambiguity for diffusion processes
AbstractIn 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1110.3897.
Date of creation: Oct 2011
Date of revision: Oct 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-11-01 (All new papers)
- NEP-MIC-2011-11-01 (Microeconomics)
- NEP-UPT-2011-11-01 (Utility Models & Prospect Theory)
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