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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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    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. Sérgio C. Bezerra & Alberto Ohashi & Francesco Russo & Francys Souza, 2020. "Discrete-type Approximations for Non-Markovian Optimal Stopping Problems: Part II," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1221-1255, September.
    3. Adesoji O. Adelaja & Ramyani Mukhopadhyay, 2022. "Time‐to‐completion for mergers and acquisitions in the food and agribusiness industry," Agribusiness, John Wiley & Sons, Ltd., vol. 38(3), pages 579-607, July.
    4. S'ergio C. Bezerra & Alberto Ohashi & Francesco Russo & Francys de Souza, 2017. "Discrete-type approximations for non-Markovian optimal stopping problems: Part II," Papers 1707.05250, arXiv.org, revised Dec 2019.
    5. 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 Jun 2019.

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