Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives

IEEE Transactions on Automatic Control

Volumn 44, Issue 10, 1999, Pages 1840-1851

  Tsitsiklis, John N ^a,b   Van Roy, Benjamin ^b  

^a IEEE   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BELLMANS EQUATION; HILBERT SPACE THEORY; OPTIMAL STOPPING PROBLEM;

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; STATE SPACE METHODS; STOCHASTIC CONTROL SYSTEMS;

OPTIMAL CONTROL SYSTEMS;

EID: 0033351917     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.793723     Document Type: Article

References (23)

1. L. C. Baird, "Residual algorithms: Reinforcement learning with function approximation," in Machine Learning: Proc. Twelfth Int. Conf., Prieditis and Russell, Eds. San Francisco, CA: Morgan Kaufman, 1995.
2. J. Barraquand and D. Martineau, "Numerical valuation of high dimensional multivariate american securities," to be published.
3. A. Benveniste, M. Metivier, and P. Priouret, Adaptive Algorithms and Stochastic Approximations. Berlin, Germany: Springer-Verlag, 1990.
4. D. P. Bertsekas, Dynamic Programming and Optimal Control. Belmont, MA: Athena Scientific, 1995.
5. D. P. Bertsekas and S. E. Shreve, Stochastic Optimal Control: The Discrete Time Case. Belmont, MA: Athena Scientific, 1996.
6. D. P. Bertsekas and J. N. Tsitsiklis, Neuro-Dynamic Programming. Belmont, MA: Athena Scientific, 1996.
7. F. Black and M. Scholes, "The pricing of options and corporate liabilities," J. Political Economy, vol. 81, pp. 637-654, 1973.
8. M. Broadie and P. Glasserman, "Pricing american-style securities using simulation," J. Economic Dynam. Contr., vol. 21, pp. 1323-1352, 1997.
9. _, "A stochastic mesh method for pricing high-dimensional american options," to be published.
10. J. M. Harrison and D. Kreps, "Martingales and arbitrage in multiperiod securities markets," J. Economic Theory, vol. 20, pp. 381-408, 1979.
11. J. M. Harrison and S. Pliska, "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and Their Appl., vol. 11, pp. 215-260, 1981.
12. I. Karatzas, "On the pricing of american options," Applied Math. Operations Res., pp. 37-60, 1988.
13. R. C. Merton, "Theory of rational option pricing," Bell J. Economics and Management Sci., vol. 4, pp. 141-183, 1973.
14. M. Parsley, "Exotics enter the mainstream," Euromoney, pp. 127-130, Mar. 1997.
15. J. Rust, "Using randomization to break the curse of dimensionality," Econometrica, 1996.
16. A. N. Shiryaev, Optimal Stopping Rules. New York: Springer-Verlag, 1978.
17. R. S. Sutton, "Learning to predict by the methods of temporal differences," Machine Learning, vol. 3, pp. 9-44, 1988.
18. _, "On the virtues of linear learning and trajectory distributions," in Proc. Workshop on Value Function Approximation, Machine Learning Conf. 1995, Boyan, Moore, and Sutton, Eds. Technical Rep. CMU-CS-95-206, Carnegie Mellon Univ., Pittsburgh, PA 15213, 1995, p. 85.
19. J. N. Tsitsiklis and B. Van Roy, "An analysis of temporal-difference learning with function approximation," IEEE Trans. Automat. Contr., May 1997.
20. _, "Approximate solutions to optimal stopping problems," in Advances in Neural Information Processing Systems 9, M. C. Mozer, M. I. Jordan, and T. Petsche, Eds. Cambridge, MA: MIT Press, 1997.
21. B. Van Roy, "Learning and value function approximation in complex decision processes," Ph.D. dissertation, MIT, June 1998.
22. C. J. C. H. Watkins, "Learning from delayed rewards," Doctoral dissertation, Univ. Cambridge, Cambridge, U.K., 1989.
23. C. J. C. H. Watkins and P. Dayan, "Q-learning," Machine Learning, vol. 8, pp. 279-292, 1992.