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Backward SDEs for control with partial information

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  • Andrew Papanicolaou

Abstract

This paper considers a non‐Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non‐Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation.

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  • Andrew Papanicolaou, 2019. "Backward SDEs for control with partial information," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 208-248, January.
    • Handle: RePEc:bla:mathfi:v:29:y:2019:i:1:p:208-248
    DOI: 10.1111/mafi.12174
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    Cited by:

    1. Dongmei Zhu & Harry Zheng, 2022. "Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 191-219, July.
    2. Chao Deng & Xizhi Su & Chao Zhou, 2020. "Relative wealth concerns with partial information and heterogeneous priors," Papers 2007.11781, arXiv.org.
    3. Sebastian Jaimungal & Xiaofei Shi, 2024. "The Price of Information," Papers 2402.11864, arXiv.org, revised Mar 2024.
    4. Elisabeth Leoff & Leonie Ruderer & Jörn Sass, 2022. "Signal-to-noise matrix and model reduction in continuous-time hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 327-359, April.

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