Abstract:
Two optimal stopping problems for geometric random walks with the observer's power payoff function, on the finite and infinite horizons, are solved. For these problems, an explicit form of the cut value and also optimal stopping rules are established. It is proved that the optimal stopping rules are nonrandomized thresholds and describe the corresponding free boundary. An explicit form of the free boundary is presented.
Keywords:geometric random walks, stopping time, stopping domain, domain of continuing observations, generating function.
Presented by the member of Editorial Board:A. I. Kibzun