Optimal decision under ambiguity for diffusion processes
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.
References listed on IDEAS
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- Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, 05.
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- Tatjana Chudjakow & Frank Riedel, 2013. "The best choice problem under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 77-97, September.
- Chudjakow, Tatjana & Riedel, Frank, 2010. "The Best Choice Problem under Ambiguity," Center for Mathematical Economics Working Papers 413, Center for Mathematical Economics, Bielefeld University.
- Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463. Full references (including those not matched with items on IDEAS)
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