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Optimal switching problems under partial information

Author

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  • Li Kai

    (Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden)

  • Nyström Kaj

    (Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden)

  • Olofsson Marcus

    (Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden)

Abstract

In this paper, we formulate and study an optimal switching problem under partial information. In our model, the agent/manager/investor attempts to maximize the expected reward by switching between different states/investments. However, he is not fully aware of his environment and only an observation process, which contains partial information about the environment/underlying, is accessible. It is based on the partial information carried by this observation process that all decisions must be made. We propose a probabilistic numerical algorithm, based on dynamic programming, regression Monte Carlo methods, and stochastic filtering theory, to compute the value function. In this paper, the approximation of the value function and the corresponding convergence result are obtained when the underlying and observation processes satisfy the linear Kalman–Bucy setting. A numerical example is included to show some specific features of partial information.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:mcmeap:v:21:y:2015:i:2:p:91-120:n:1
    DOI: 10.1515/mcma-2014-0013
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    References listed on IDEAS

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    1. Aïd, René & Campi, Luciano & Langrené, Nicolas & Pham, Huyên, 2014. "A probabilistic numerical method for optimal multiple switching problems in high dimension," LSE Research Online Documents on Economics 63011, London School of Economics and Political Science, LSE Library.
    2. 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.
    3. Gassiat, Paul & Kharroubi, Idris & Pham, Huyên, 2012. "Time discretization and quantization methods for optimal multiple switching problem," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2019-2052.
    4. René Aïd & Luciano Campi & Nicolas Langrené & Huyên Pham, 2014. "A probabilistic numerical method for optimal multiple switching problems in high dimension," Post-Print hal-02294328, HAL.
    5. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
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