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Optimal decision under ambiguity for diffusion processes

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  • S\"oren Christensen
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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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    File URL: http://arxiv.org/pdf/1110.3897
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.3897.

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    Date of creation: Oct 2011
    Date of revision: Oct 2012
    Handle: RePEc:arx:papers:1110.3897

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    Web page: http://arxiv.org/

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    1. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
    2. Tatjana Chudjakow & Frank Riedel, 2013. "The best choice problem under ambiguity," Economic Theory, Springer, vol. 54(1), pages 77-97, September.
    3. Luis H. R. Alvarez E., 2006. "A Class of Solvable Stopping Games," Discussion Papers 11, Aboa Centre for Economics.
    4. Xue Cheng & Frank Riedel, 2010. "Optimal Stopping Under Ambiguity in Continuous Time," Working Papers 429, Bielefeld University, Center for Mathematical Economics.
    5. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, 05.
    6. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    7. Erik Ekstr\"{o}m & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
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