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A simulation approach to optimal stopping under partial information

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  • Ludkovski, Michael

Abstract

We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional diffusion with correlated noise. Such models where the controller is not fully aware of her environment are of interest in applied probability and financial mathematics. We propose a new approximate numerical algorithm based on the particle filtering and regression Monte Carlo methods. The algorithm maintains a continuous state space and yields an integrated approach to the filtering and control sub-problems. Our approach is entirely simulation-based and therefore allows for a robust implementation with respect to model specification. We carry out the error analysis of our scheme and illustrate with several computational examples. An extension to discretely observed stochastic volatility models is also considered.

Suggested Citation

  • Ludkovski, Michael, 2009. "A simulation approach to optimal stopping under partial information," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4061-4087, December.
  • Handle: RePEc:eee:spapps:v:119:y:2009:i:12:p:4061-4087
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
    3. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    4. repec:spr:compst:v:50:y:1999:i:1:p:135-147 is not listed on IDEAS
    5. Pham Huyên & Runggaldier Wolfgang & Sellami Afef, 2005. "Approximation by quantization of the filter process and applications to optimal stopping problems under partial observation," Monte Carlo Methods and Applications, De Gruyter, vol. 11(1), pages 57-81, March.
    6. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    7. Giuseppe Moscarini & Lones Smith, 2001. "The Optimal Level of Experimentation," Econometrica, Econometric Society, vol. 69(6), pages 1629-1644, November.
    8. Jakv{s}a Cvitani'c & Robert Liptser & Boris Rozovskii, 2006. "A filtering approach to tracking volatility from prices observed at random times," Papers math/0612212, arXiv.org.
    9. Peter Muller & Bruno Sanso & Maria De Iorio, 2004. "Optimal Bayesian Design by Inhomogeneous Markov Chain Simulation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 788-798, January.
    10. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Cited by:

    1. Li Kai & Nyström Kaj & Olofsson Marcus, 2015. "Optimal switching problems under partial information," Monte Carlo Methods and Applications, De Gruyter, vol. 21(2), pages 91-120, June.
    2. S'ergio C. Bezerra & Alberto Ohashi & Francesco Russo, 2017. "Discrete-type approximations for non-Markovian optimal stopping problems: Part II," Papers 1707.05250, arXiv.org, revised Jan 2018.
    3. Dorival Le~ao & Alberto Ohashi & Francesco Russo, 2017. "Discrete-type approximations for non-Markovian optimal stopping problems: Part I," Papers 1707.05234, arXiv.org, revised Jan 2018.

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