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Tr. Mat. Inst. Steklova, 2014, Volume 287, Pages 310–319 (Mi tm3578)  

On the existence of solutions of unbounded optimal stopping problems

M. V. Zhitlukhinab, A. N. Shiryaevca

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b International Laboratory of Quantitative Finance, National Research University Higher School of Economics, Moscow, Russia
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia

Abstract: 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 $G(\tau,B_\tau)=|B_\tau|-c/(1-\tau)$.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-31468-mol_a
14-01-00739
Russian Science Foundation 14-21-00162
The first author was supported by the Russian Foundation for Basic Research, project nos. 14-01-31468-mol_a and 14-01-00739. The second author was supported by the Russian Science Foundation, project no. 14-21-00162.


DOI: https://doi.org/10.1134/S0371968514040189

Full text: PDF file (217 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 287:1, 299–307

Bibliographic databases:

Document Type: Article
UDC: 519.244
Received in October 2014

Citation: M. V. Zhitlukhin, A. N. Shiryaev, “On the existence of solutions of unbounded optimal stopping problems”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 310–319; Proc. Steklov Inst. Math., 287:1 (2014), 299–307

Citation in format AMSBIB
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\paper On the existence of solutions of unbounded optimal stopping problems
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\bookinfo Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday
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\vol 287
\pages 310--319
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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