Optimal stopping times with different information levels and with time uncertainty
نویسندگان
چکیده
Optimization/control problems with change of filtartions have been studied in various context of mathematical finance. This paper studies optimal stopping problems for general diffusion processes with an uncertain time horizon and under different filtrations. Corresponding value functions are first compared and related explicitly to their counterparts without the time uncertainty. To further analyze optimal stopping strategies, characterization results regarding connectivity of the “stopping” and “continuation” regions are derived. In particular, sufficient conditions for the well-known “threshold type” optimal stopping rule are given. Finally, optimal stopping problems with standard American call/put type payoffs are revisited using these characterization results. ∗Statistics and Mathematics Unit, Indian Statistical Institute, 7 S.J.S. Sansanwal Marg, New Delhi 110016, India, Phone +91-11-41493918, email: [email protected]. †Department of Industrial Engineering and Operations Research, UC Berkeley, CA 94720-1777, USA, Phone (510) 642 3615, email: [email protected].
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