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Stochastic filtering of a pure jump process with predictable jumps and path-dependent local characteristics

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  • Bandini, Elena
  • Calvia, Alessandro
  • Colaneri, Katia

Abstract

The objective of this paper is to study the filtering problem for a system of partially observable processes (X, Y), where X is a non-Markovian pure jump process representing the signal and Y is a general jump diffusion which provides observations. Our model covers the case where both processes are not necessarily quasi left-continuous, allowing them to jump at predictable stopping times. By introducing the Markovian version of the signal, we are able to compute an explicit equation for the filter via the innovations approach.

Suggested Citation

  • Bandini, Elena & Calvia, Alessandro & Colaneri, Katia, 2022. "Stochastic filtering of a pure jump process with predictable jumps and path-dependent local characteristics," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 396-435.
    • Handle: RePEc:eee:spapps:v:151:y:2022:i:c:p:396-435
    DOI: 10.1016/j.spa.2022.06.007
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    References listed on IDEAS

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    1. Suhan Altay & Katia Colaneri & Zehra Eksi, 2017. "Pairs Trading under Drift Uncertainty and Risk Penalization," Papers 1704.06697, arXiv.org, revised Sep 2018.
    2. Sühan Altay & Katia Colaneri & Zehra Eksi, 2018. "Pairs Trading Under Drift Uncertainty And Risk Penalization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-24, November.
    3. Bandini, Elena & Cosso, Andrea & Fuhrman, Marco & Pham, Huyên, 2019. "Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 674-711.
    4. Colaneri, Katia & Eksi, Zehra & Frey, Rüdiger & Szölgyenyi, Michaela, 2020. "Optimal liquidation under partial information with price impact," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1913-1946.
    5. Fontana, Claudio & Schmidt, Thorsten, 2018. "General dynamic term structures under default risk," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3353-3386.
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