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2013 | 42 | nr 3 | 593--612
Tytuł artykułu

Optimal Stopping Model with Unknown Transition Probabilities

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article concerns the optimal stopping problem for a discrete-time Markov chain with observable states, but with unknown transition probabilities. A stopping policy is graded via the expected total-cost criterion resulting from the non-negative running and terminal costs. The Dynamic Programming method, combined with the Bayesian approach, is developed. A series of explicitly solved meaningful examples illustrates all the theoretical issues. (original abstract)
Rocznik
Tom
42
Numer
Strony
593--612
Opis fizyczny
Twórcy
  • Kanagawa University, Japan
  • University of Liverpool, United Kingdom
Bibliografia
  • Bäuerle, N. and Rieder, U. (2011) Markov Decision Processes with Applications to Finance. Springer-Verlag, Berlin.
  • Bertsekas, D.P. and Shreve, S.E. (1978) Stochastic Optimal Control. Academic Press, New York.
  • Dufour, F. and Piunovskiy, A. (2010) Multiobjective stopping problem for discrete-time Markov processes: the convex analytic approach. Journal of Applied Probability 47: 947-966.
  • Dynkin, E.B. and Yushkevich A.A. (1979) Controlled Markov Processes and their Applications. Springer-Verlag, New York - Berlin.
  • Easley, D. and Kiefer, N.M. (1988) Controlling a stochastic process with unknown parameters. Econometrica 56: 1045-1064.
  • Ekström, E. and Lu, B. (2011) Optimal selling of an asset under incomplete information. Int. J. Stoch. Anal. Art. ID 543590, 17 ,2090-3340.
  • Ferguson, T.S. (1967) Mathematical Statistics. Academic Press, New York- London.
  • González-Trejo, J.I., Hernández-Lerma, O. and Hoyos-Reyes, L.F. (2003) Minimax control of discrete-time stochastic systems. SIAM J.Control Optim 41: 1626-1659.
  • DeGroot, M.H. (1970) Optimal Statistical Decisions. McGraw-Hill Book Co., New York.
  • van Hee, K.M. (1978) Bayesian Control of Markov Chains. Mathematical Centre Tracts, No. 95. Mathematisch Centrum, Amsterdam.
  • Hernández-Lerma, O. and Marcus, S.I. (1985) Adaptive control of discounted Markov decision chains. Journal of Optimization Theory and Applications 46: 227-235.
  • Hernández-Lerma, O. (1989) Adaptive Markov Control Processes, volume 79 of Applied Mathematical Sciences. Springer-Verlag, New York.
  • Hernández-Lerma, O. and Lasserre, J.B. (1996) Discrete-time Markov Control Processes. Springer, New York.
  • Hordijk, A. (1974) Dynamic Programming and Markov Potential Theory. Mathematical Centre Tracts, No. 51. Mathematisch Centrum, Amsterdam.
  • Horiguchi, M. (2001a) Markov decision processes with a stopping time constraint. Mathematical Methods of Operations Research 53: 279-295.
  • Horiguchi, M. (2001b) Stopped Markov decision processes with multiple constraints. Mathematical Methods of Operations Research 54: 455-469.
  • Kurano, M. (1972) Discrete-time Markovian decision processes with an unknown parameter. Average return criterion. Journal of the Operations Research Society of Japan 15: 67-76.
  • Kurano, M. (1983) Adaptive policies in Markov decision processes with uncertain transition matrices. Journal of Information & Optimization Sciences 4: 21-40
  • Mandl, P. (1974) Estimation and control in Markov chains. Advances in Applied Probability 6: 40-60.
  • Martin, J.J. (1967) Bayesian Decision Problems and Markov Chains. Publications in Operations Research, No. 13. John Wiley & Sons Inc., New York.
  • Piunovskiy, A. B. (2006) Dynamic programming in constrained Markov decision processes. Control and Cybernetics 35: 645-660.
  • Puterman, M. (1994) Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York.
  • Raiffa, H and Schlaifer, R. (1961) Applied Statistical Decision Theory. Studies in Managerial Economics. Division of Research, Graduate School of Business Administration, Harvard University, Boston, Mass.
  • Rieder, U. (1975) Bayesian Dynamic Programming. Advances in Applied Probability 7: 330-348.
  • Ross, S.M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.
  • Ross, S.M. (1983) Introduction to Stochastic Dynamic Programming. Academic Press, San Diego, CA.
  • Stadje, W. (1997) An optimal stopping problem with two levels of incomlete information. Mathem. Methods of Oper. Research 45: 119-131.
  • Wald, A. (1950) Statistical Decision Functions. John Wiley & Sons Inc., New York.
  • Wang, X. and Yi, Y. (2009) An optimal investment and consumption model with stochastic returns. Applied Stoch. Models in Business and Industry 25: 45-55.
  • White, D.J. (1969) Dynamic Programming. Mathematical Economic Texts, 1. Oliver&Boyd, Edinburgh-London.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ekon-element-000171325771

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