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BSDEs under partial information and financial applications

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  • Ceci, Claudia
  • Cretarola, Alessandra
  • Russo, Francesco

Abstract

In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square-integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted information can be derived by that related to a problem of a BSDE under full information. In particular, we provide a suitable version of the Föllmer–Schweizer decomposition of a square-integrable random variable working under partial information and we use this achievement to investigate the local risk-minimization approach for a semimartingale financial market model.

Suggested Citation

  • Ceci, Claudia & Cretarola, Alessandra & Russo, Francesco, 2014. "BSDEs under partial information and financial applications," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2628-2653.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2628-2653
    DOI: 10.1016/j.spa.2014.03.003
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Rüdiger Frey & Thorsten Schmidt, 2012. "Pricing and hedging of credit derivatives via the innovations approach to nonlinear filtering," Finance and Stochastics, Springer, vol. 16(1), pages 105-133, January.
    3. Martin Schweizer, 1994. "Risk‐Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342, October.
    4. Claudia Ceci, 2012. "Utility Maximization With Intermediate Consumption Under Restricted Information For Jump Market Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-34.
    5. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    6. Briand, Philippe & Delyon, Bernard & Mémin, Jean, 2002. "On the robustness of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 229-253, February.
    7. Rüdiger Frey, 2000. "Risk Minimization with Incomplete Information in a Model for High‐Frequency Data," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 215-225, April.
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    Cited by:

    1. Martin Schweizer & Danijel Zivoi & Mario Šikić, 2018. "Dynamic Mean–Variance Optimization Problems With Deterministic Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, March.
    2. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2015. "Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 47-60.
    3. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.
    4. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2015. "The F\"ollmer-Schweizer decomposition under incomplete information," Papers 1511.05465, arXiv.org, revised Mar 2016.
    5. Yao, Song, 2017. "Lp solutions of backward stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3465-3511.
    6. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2017. "Unit-linked life insurance policies: Optimal hedging in partially observable market models," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 149-163.
    7. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2016. "Unit-linked life insurance policies: optimal hedging in partially observable market models," Papers 1608.07226, arXiv.org, revised Dec 2016.

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