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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Tatjana Chudjakow & Frank Riedel, 2013.
"The best choice problem under ambiguity,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 77-97, September.
- Epstein, Larry G. & Schneider, Martin, 2003.
Journal of Economic Theory,
Elsevier, vol. 113(1), pages 1-31, November.
- Erik Ekstr\"om & Stephane Villeneuve, 2006.
"On the value of optimal stopping games,"
- Luis H. R. Alvarez E., 2006. "A Class of Solvable Stopping Games," Discussion Papers 11, Aboa Centre for Economics.
- Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
- Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, 05.
- Riedel, Frank, 2010. "Optimal Stopping under Ambiguity in Continuous Time," Center for Mathematical Economics Working Papers 429, Center for Mathematical Economics, Bielefeld University.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1110.3897. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.