This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
 References
Ainlar, E.: Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ (1975)
Chow, Y.S., Robbins H., Sigmund D.: Great Expectations: The Theory of Opti-mal Stopping. Houghton Mifflin Co., NY (1971)
Davis, M., Karatzas I.: A deterministic Approach to Optimal Stopping. In: Kelly F.P. (ed) Probability, Statistics and Optimization. Wiley&Sons, NY (1994)
Dynkin, E.B., Yushkevich A.A.: Markov Processes. Theorems and Problems. Plenum Press, New York (1969)
Ferguson, T.S.: Optimal Stoppingand Applications . (Electronic text on a web-site).
Kemeny, J.G., Snell J.L.: Finite Markov chains. Van Nostrand Reinhold, Prince-ton, NJ (1960)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Pro-gramming. Wiley, New York (1994)
Sheskin, T.J.: State reduction in a Markov decision process. Internat. J. Math. Ed. Sci. Tech. 30, no. 2, 167-185 (1999)
Shiryaev, A.N.: Statistical Sequential Analysis: Optimal StoppingRules . (In Russian), Izdat. Nauka, Moscow (1969)
Shiryayev, A.N.: Optimal StoppingRules . Springer-Verlag, New York (1978)
Sonin, I.M.: Two simple theorems in the problems of optimal stopping. In: Proc. INFORMS Appl. Prob. Conf., Atlanta, Georgia (1995)
Sonin, I.M.: The Elimination Algorithm for the problem of optimal stopping. Math. Meth. of Oper. Res., 49, no. 1, 111-123 (1999)
Sonin, I.M.: The State Reduction and related algorithms and their applications to the study of Markov chains, graph theory and the Optimal Stopping problem. Advances in Mathematics 145, no. 2, 159-188, Princeton, NJ (1999)
Sonin, I.M.: A Generalized Gittins index for Markov chain and its recursive calculation. Manuscript (2004)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sonin, I.M. (2006). The Optimal Stopping of a Markov Chain and Recursive Solution of Poisson and Bellman Equations. In: From Stochastic Calculus to Mathematical Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30788-4_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-30788-4_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30782-2
Online ISBN: 978-3-540-30788-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)