Optimal Stopping for Dynamic Convex Risk Measures

Illinois Journal of Mathematics, 54, 1025-1067, 2010

43 Pages Posted: 16 Feb 2014 Last revised: 8 Jul 2016

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Ioannis Karatzas

Columbia University - Department of Statistics

Song Yao

University of Pittsburgh

Date Written: September 27, 2009

Abstract

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who chooses the termination time of the game, and an agent (the "controller", or "Nature") who selects the probability measure.

Keywords: Convex risk measures, continuous-time optimal stopping, robustness methods, zero sum games, saddle point, reflected backward stochastic differential equations, BMO martingales

Suggested Citation

Bayraktar, Erhan and Karatzas, Ioannis and Yao, Song, Optimal Stopping for Dynamic Convex Risk Measures (September 27, 2009). Illinois Journal of Mathematics, 54, 1025-1067, 2010. Available at SSRN: https://ssrn.com/abstract=2395442

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Ioannis Karatzas

Columbia University - Department of Statistics ( email )

Mail Code 4403
2990 Broadway, Room 618
New York, NY 10027
United States
212-854-3177 (Phone)
212-663-2454 (Fax)

Song Yao

University of Pittsburgh ( email )

507 Thackeray Hall
Pittsburgh, PA 15260
United States

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