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Backward stochastic differential equations with enlarged filtration: Option hedging of an insider trader in a financial market with jumps

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  • Anne Eyraud-Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

Insider trading consists in having an additional information, unknown from the common investor, and using it on the financial market, in order to improve the wealth of a portfolio. Mathematical model-ing can study such behaviors, by modeling this additional information within the market, and comparing the investment strategies of an insider trader and a non informed investor. Research on this subject has already been carried out by A. Grorud and M. Pontier since 1996, studying the problem in a wealth optimization point of view. This work focuses more on option hedging problems. We have chosen to study wealth equations as backward stochastic differential equations (BSDE), and we use Jeulin's method of enlargement of filtration to model the information of our insider trader. We will try to compare the strategies of an insider trader and a non insider one. Different models are studied: at first prices are driven only by a Brownian motion, and in a second part, we add jump processes (Poisson point processes) to the model.

Suggested Citation

  • Anne Eyraud-Loisel, 2005. "Backward stochastic differential equations with enlarged filtration: Option hedging of an insider trader in a financial market with jumps," Post-Print hal-01298905, HAL.
    • Handle: RePEc:hal:journl:hal-01298905
    DOI: 10.1016/j.spa.2005.05.006
    Note: View the original document on HAL open archive server: https://hal.science/hal-01298905
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    References listed on IDEAS

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    1. Axel Grorud & Monique Pontier, 1998. "Insider Trading in a Continuous Time Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 331-347.
    2. Bardhan, Indrajit & Chao, Xiuli, 1996. "On martingale measures when asset returns have unpredictable jumps," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 35-54, October.
    3. Axel Grorud & Monique Pontier, 2001. "Asymmetrical Information And Incomplete Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 285-302.
    4. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    5. Axel Grorud, 2000. "Asymmetric Information In A Financial Market With Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 641-659.
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    Citations

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    Cited by:

    1. Anne Eyraud-Loisel, 2013. "Quadratic hedging in an incomplete market derived by an influent informed investor," Post-Print hal-00450949, HAL.
    2. Jiang Wu & Fucheng Liao & Masayoshi Tomizuka, 2017. "Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(1), pages 129-137, January.
    3. Dela Vega, Engel John C. & Elliott, Robert J., 2022. "Backward stochastic differential equations with regime-switching and sublinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 278-298.
    4. Lorenc Kapllani & Long Teng, 2020. "Deep learning algorithms for solving high dimensional nonlinear backward stochastic differential equations," Papers 2010.01319, arXiv.org, revised Jun 2022.
    5. Anne Eyraud-Loisel, 2011. "Option Hedging By An Influent Informed Investor," Post-Print hal-00450948, HAL.
    6. Anne Eyraud-Loisel, 2019. "How Does Asymmetric Information Create Market Incompleteness?," Post-Print hal-01998386, HAL.
    7. Fontana, Claudio, 2018. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1007-1033.
    8. Anne Eyraud-Loisel, 2019. "How Does Asymmetric Information Create Market Incompleteness?," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 531-538, June.
    9. Madan, Dilip & Pistorius, Martijn & Stadje, Mitja, 2016. "Convergence of BSΔEs driven by random walks to BSDEs: The case of (in)finite activity jumps with general driver," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1553-1584.
    10. Bouchard, Bruno & Elie, Romuald, 2008. "Discrete-time approximation of decoupled Forward-Backward SDE with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 53-75, January.
    11. Behzad Alimoradian & Karim Barigou & Anne Eyraud-Loisel, 2022. "Derivatives under market impact: Disentangling cost and information," Working Papers hal-03668432, HAL.

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