Principles of optimal stopping and free-boundary problems (Q2784224)

This thesis studies optimal stopping problems for Markov processes by reducing them to free-boundary problems. The thesis consists of twenty-two papers that the author wrote (some with A. N. Shiryaev, S. E. Graverson, J. L. Pedersen, cf. list of papers, p. vii) on the subject in the period 1994-2000. The four most illustrative papers are presented in Chapters 2-5. These chapters also contain 17 figures. A short description of each paper with some historical remarks is given in Chapter 1. In this chapter the author also presents the origin and history of optimal stopping for Markov processes and related problems, indicates their interplay and applications, and presents a survey of the papers (Section 1.2) which form the thesis.