Constrained dynkin's stopping problem with continuous parameter

Abstract

We consider Dynkin's stopping problem with a finite constraint for right continuous, adapted and bounded processes. In general the minimax value process of the problem does not coincide with the maximin one. We show that there exists a right continuous version of the minimax (maximin) value process, and that the version is the smallest (largest) among right continuous processes satisfying certain stopped martingale inequalities. We then give equivalent conditions for the coincidence of two value processes. The proof of these results is reduced to certain Dynkin's problem without a finite constraint.

Keywords:

• Dynkin's game
• minimax value process
• aggregation
• finite constraint
• stopped martingale
• saddle point

^*This research is Partially supported by Grant-in Aid For encouragement of young Scientists A-62740127 from The Ministry of Education, Science and Culture of Japan

^*This research is Partially supported by Grant-in Aid For encouragement of young Scientists A-62740127 from The Ministry of Education, Science and Culture of Japan

Notes

^*This research is Partially supported by Grant-in Aid For encouragement of young Scientists A-62740127 from The Ministry of Education, Science and Culture of Japan