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Partially observed optimal stopping problem for discrete-time Markov processes

Author

Listed:
  • Benoîte Saporta

    (IMAG)

  • François Dufour

    (INRIA)

  • Christophe Nivot

    (INRIA)

Abstract

This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization procedure based on optimal quantization. First, we discretize the state space of the unobserved variable by quantizing an underlying reference measure. Then we jointly discretize the resulting approximate filter and the observation process. We obtain a fully computable approximation of the value function with explicit error bounds for its convergence towards the true value function.

Suggested Citation

  • Benoîte Saporta & François Dufour & Christophe Nivot, 2017. "Partially observed optimal stopping problem for discrete-time Markov processes," 4OR, Springer, vol. 15(3), pages 277-302, September.
    • Handle: RePEc:spr:aqjoor:v:15:y:2017:i:3:d:10.1007_s10288-016-0337-8
    DOI: 10.1007/s10288-016-0337-8
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    References listed on IDEAS

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    1. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
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    Cited by:

    1. Fang Chen & Xianping Guo & Zhong-Wei Liao, 2022. "Optimal Stopping Time on Semi-Markov Processes with Finite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 408-439, August.

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