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Discrete Time Approximations of Continuous Time Finite Horizon Stopping Problems

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Optimization, Control, and Applications of Stochastic Systems

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

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Abstract

In this chapter, we approximate continuous time finite horizon stopping problems using either continuous and discrete time penalty approach or direct discretization. We point out possible errors of such approximations and construct approximate optimal stopping times.

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References

  1. Bensoussan, A., Lions, J.L.: Applications of Variational Inequalities in Stochastic Control. Elsevier North Holland (1982)

    Google Scholar 

  2. Davis, M., Karatzas, I.: A deterministic approach to optimal stopping with applications to a prophet inequality. P. Whittle Festschrift, in Wiley Ser. Probab. Math. Statist. Probab. Math. Statist., Wiley, Chichester, 455–466 (1994)

    Google Scholar 

  3. Dynkin, E.B.: Markov processes. Berlin, Gottingen, Heidelberg, Springer (1965)

    MATH  Google Scholar 

  4. Fakeev, A.G.: On the question of the optimal stopping of a Markov process. (Russian) Teor. Verojatnost. i Primenen. 16, 708-710 (1971)

    Google Scholar 

  5. Haugh, M.B., Kogan, L.: Pricing American Options: a Duality Approach. Operations Research 52, 258–270 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Krylov, N.V.: The problem with two free boundaries for an elliptic equation and optimal stopping of Markov processes. Dokl. Akad. Nauk USSR 194, 1263–1265 (1970)

    Google Scholar 

  7. Meyer, P.A.: Processes de Markov, LNM 26, Berlin, Heidelberg, New York, Springer (1967)

    Book  Google Scholar 

  8. Palczewski, J., Stettner, L.: Finite Horizon Optimal Stopping of Time - Discontinuous Functionals with Applications to Impulse Control with Delay. SIAM J. Control Optim. 48, 4874–4909 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Palczewski, J., Stettner, L.: Stopping of discontinuous functionals with the first exit time discontinuity. Stoch. Proc. Their Appl., 121, 2361–2392 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Robin, M.: Controle impulsionnel des processus de Markov (Thesis), University of Paris IX (1978)

    Google Scholar 

  11. Rogers, L.C.G.: Monte Carlo Valuation of American Options. Mathematical Finance 12, 271–286 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Rogers, L.C.G.: Dual Valuation and Hedging of Bermidian Options. SIAM J. Financial Math. 1, 604–608 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Stettner, L.: Zero-sum markov Games with Stopping and Impulsive Strategies. Appl. Math. Optimiz. 9, 1–24 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  14. Stettner, L.: Penalty method for finite horizon stopping problems. SIAM J. Control Optim. 49, 1078–1999 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Research supported by MNiSzW grant NN 201 371836.

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Authors and Affiliations

  1. Institute of Mathematics Polish Academy of Sciences, 00-956, Warsaw, Poland

    Lukasz Stettner

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  1. Lukasz Stettner
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Correspondence to Lukasz Stettner .

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Editors and Affiliations

  1. , Department of Probability and Statistics, Center for Research in Mathematics, Jalisco s/n, Guanajuato, 36000, Mexico

    Daniel Hernández-Hernández

  2. , Department of Mathematics, University of Sonora, Rosales s/n, Hermosillo, 83000, Sonora, Mexico

    J. Adolfo Minjárez-Sosa

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Stettner, L. (2012). Discrete Time Approximations of Continuous Time Finite Horizon Stopping Problems. In: Hernández-Hernández, D., Minjárez-Sosa, J. (eds) Optimization, Control, and Applications of Stochastic Systems. Systems & Control: Foundations & Applications. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8337-5_16

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