IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1806.04025.html
   My bibliography  Save this paper

BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets

Author

Listed:
  • Yushi Hamaguchi

Abstract

We consider Lipschitz-type backward stochastic differential equations (BSDEs) driven by cylindrical martingales on the space of continuous functions. We show the existence and uniqueness of the solution of such infinite-dimensional BSDEs and prove that the sequence of solutions of corresponding finite-dimensional BSDEs approximates the original solution. We also consider the hedging problem in bond markets and prove that, for an approximately attainable contingent claim, the sequence of locally risk-minimizing strategies based on small markets converges to the generalized hedging strategy.

Suggested Citation

  • Yushi Hamaguchi, 2018. "BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets," Papers 1806.04025, arXiv.org.
    • Handle: RePEc:arx:papers:1806.04025
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1806.04025
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marzia Donno & Maurizio Pratelli, 2004. "On the use of measure-valued strategies in bond markets," Finance and Stochastics, Springer, vol. 8(1), pages 87-109, January.
    2. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    3. repec:dau:papers:123456789/12663 is not listed on IDEAS
    4. 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.
    5. De Donno, M. & Guasoni, P. & Pratelli, M., 2005. "Super-replication and utility maximization in large financial markets," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 2006-2022, December.
    6. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    2. Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
    3. 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.
    4. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
    5. Wanyang Dai, 2014. "Mean-variance hedging based on an incomplete market with external risk factors of non-Gaussian OU processes," Papers 1410.0991, arXiv.org, revised Aug 2015.
    6. repec:dau:papers:123456789/5374 is not listed on IDEAS
    7. Scott Robertson & Konstantinos Spiliopoulos, 2014. "Indifference pricing for Contingent Claims: Large Deviations Effects," Papers 1410.0384, arXiv.org, revised Feb 2016.
    8. Sai Hung Marten Ting & Christian-Oliver Ewald, 2013. "On the performance of asymptotic locally risk minimising hedges in the Heston stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 939-954, May.
    9. Ewald, Christian Oliver & Taub, Bart, 2022. "Real options, risk aversion and markets: A corporate finance perspective," Journal of Corporate Finance, Elsevier, vol. 72(C).
    10. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," JRFM, MDPI, vol. 8(1), pages 1-20, February.
    11. Rolf Poulsen & Klaus Reiner Schenk-Hoppe & Christian-Oliver Ewald, 2009. "Risk minimization in stochastic volatility models: model risk and empirical performance," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 693-704.
    12. Oleksii Mostovyi, 2014. "Utility maximization in the large markets," Papers 1403.6175, arXiv.org, revised Oct 2014.
    13. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    14. Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
    15. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    16. Masaaki Fujii & Akihiko Takahashi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 283-304, September.
    17. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    18. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    19. Mingyu Xu, 2007. "Reflected Backward SDEs with Two Barriers Under Monotonicity and General Increasing Conditions," Journal of Theoretical Probability, Springer, vol. 20(4), pages 1005-1039, December.
    20. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Pricing and hedging contingent claims using variance and higher order moment swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 531-550, April.
    21. Gobet, Emmanuel & Labart, Céline, 2007. "Error expansion for the discretization of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 803-829, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1806.04025. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.