Representation results for jump processes with application to optimal stopping

Abstract

It is shown that functions, measurable on the past of a jump process up to a stopping time, can be expressed as functions of the jump times and jump locations up to the stopping time. These results lead to formulas for conditional expectations with respect to the past of the process up to the stopping time. The use of these results is illustrated in giving a sufficient condition for optimality for optimal stopping of a partially observed jump Markov process.

^†The author is a member of the SFB 72 of the Deutsche Forschungsgemeinschaft, Bonn

^‡The author's work was supported by NSF Grant ENG-7904444

^§The author's work was partially supported by SFB 72 of the Deutsche Forschungsgemeinschaft and partially supported by NSF Grant ENG-7904444

^†The author is a member of the SFB 72 of the Deutsche Forschungsgemeinschaft, Bonn

^‡The author's work was supported by NSF Grant ENG-7904444

^§The author's work was partially supported by SFB 72 of the Deutsche Forschungsgemeinschaft and partially supported by NSF Grant ENG-7904444

Notes

^†The author is a member of the SFB 72 of the Deutsche Forschungsgemeinschaft, Bonn

^‡The author's work was supported by NSF Grant ENG-7904444

^§The author's work was partially supported by SFB 72 of the Deutsche Forschungsgemeinschaft and partially supported by NSF Grant ENG-7904444