On the existence of solutions of unbounded optimal stopping problems
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Known conditions of existence of solutions of optimal stopping problems for Markov processes assume that payoff functions are bounded in some sense. In this paper we prove weaker conditions which are applicable to unbounded payoff functions. The results obtained are applied to the optimal stopping problem for a Brownian motion with the payoff function G(τ,G τ)=|G τ|-c/(1-τ).
KeywordsBrownian Motion Function Versus STEKLOV Institute Lower Semicontinuous Standard Brownian Motion
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- 2.H. Chernoff, “Sequential tests for the mean of a normal distribution,” in Proc. Fourth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California Press, Berkeley, 1961), Vol. 1, pp. 79–91.Google Scholar
- 6.E. B. Dynkin, Foundations of the Theory of Markov Proceses (Fizmatgiz, Moscow, 1959). Engl. transl.: Theory of Markov Processes (Pergamon, Oxford, 1961).Google Scholar
- 11.A. N. Shiryaev, Probability, 3rd ed. (MTsNMO, Moscow, 2004) [in Russian].Google Scholar
- 12.M. V. Zhitlukhin, “Sequential methods of testing statistical hypotheses and detecting changepoints,” Cand. Sci. (Phys.-Math.) Dissertation (Steklov Math. Inst., Moscow, 2013).Google Scholar