Optimal Stopping Problem in a Model with Compensated Refusal of Reward

R. V. Ivanov

Institute of Control Sciences, Russian Academy of Sciences

Abstract: We consider the optimal stopping problem with a possible compensated refusal of reward. We discuss functionals of exponential Brownian motion. The optimal stopping time is defined on the set of all finite stopping times. The functionals under consideration correspond to payments for standard American options.

Keywords: optimal stopping problem, stopping time, exponential Brownian motion, standard American option, reward function, Itô–Meyer formula, dominated convergence.

UDC: 519.21

Received: 09.07.2008
Revised: 19.04.2010

DOI: 10.4213/mzm5261

 English version: Mathematical Notes, 2011, 89:2, 238–244

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