IDEAS home Printed from https://ideas.repec.org/p/cfi/fseres/cf440.html
   My bibliography  Save this paper

Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers (Forthcoming in Stochastics and Dynamics) (Revised version of F-431)

Author

Listed:
  • Masaaki Fujii

    (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo)

Abstract

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple (Y, Z, ψ) where Y is a semimartingale, and (Z, ψ) are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of Y's future paths, as well as quadratic and exponential growth on the spot values of (Z, ψ), respectively. The existence of the unique solution is proved for Markovian and non-Markovian settings with different structural assumptions on the driver. In the former case, some regularities on (Z, ψ) with respect to the forward process are also obtained.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2018. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers (Forthcoming in Stochastics and Dynamics) (Revised version of F-431)," CARF F-Series CARF-F-440, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf440
    as

    Download full text from publisher

    File URL: https://www.carf.e.u-tokyo.ac.jp/admin/wp-content/uploads/2018/07/F440.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    2. Olivier Menoukeu Pamen, 2015. "Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 998-1031, December.
    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. Masaaki Fujii & Akihiko Takahashi, 2018. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers (Revised version of F-409)," CARF F-Series CARF-F-431, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Olivier Menoukeu-Pamen & Romuald Hervé Momeya, 2017. "A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 349-388, June.
    3. Buss, Adrian, 2013. "Capital controls and international financial stability: a dynamic general equilibrium analysis in incomplete markets," Working Paper Series 1578, European Central Bank.
    4. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    5. Athanasopoulos, George & de Carvalho Guillén, Osmani Teixeira & Issler, João Victor & Vahid, Farshid, 2011. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Journal of Econometrics, Elsevier, vol. 164(1), pages 116-129, September.
    6. Mumtaz, Haroon & Theodoridis, Konstantinos, 2017. "Common and country specific economic uncertainty," Journal of International Economics, Elsevier, vol. 105(C), pages 205-216.
    7. Benigno, Pierpaolo & Paciello, Luigi, 2014. "Monetary policy, doubts and asset prices," Journal of Monetary Economics, Elsevier, vol. 64(C), pages 85-98.
    8. Karen K. Lewis, 2011. "Global Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 3(1), pages 435-466, December.
    9. Stefano d¡¦Addona, 2018. "Rational Ignorance in Long-run Risk Models," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 17(1), pages 43-54, June.
    10. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    11. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    12. Basso, Henrique S. & Jimeno, Juan F., 2021. "From secular stagnation to robocalypse? Implications of demographic and technological changes," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 833-847.
    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. Benjamin Eden, 2004. "Substitution and Risk Aversion: Is Risk Aversion Important for Understanding Asset Prices?," Vanderbilt University Department of Economics Working Papers 0422, Vanderbilt University Department of Economics.
    15. Aase, Knut K., 2023. "Optimal spending of a wealth fund in the discrete time life cycle model," Discussion Papers 2023/7, Norwegian School of Economics, Department of Business and Management Science.
    16. Bommier, Antoine & Lanz, Bruno & Zuber, Stéphane, 2015. "Models-as-usual for unusual risks? On the value of catastrophic climate change," Journal of Environmental Economics and Management, Elsevier, vol. 74(C), pages 1-22.
    17. Epstein, Larry G. & Zin, Stanley E., 2001. "The independence axiom and asset returns," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 537-572, December.
    18. Toshiaki Ogawa & Masato Ubukata & Toshiaki Watanabe, 2020. "Stock Return Predictability and Variance Risk Premia around the ZLB," IMES Discussion Paper Series 20-E-09, Institute for Monetary and Economic Studies, Bank of Japan.
    19. Michal Pakos & Hui Chen, 2008. "Asset Pricing with Uncertainty About the Long Run," 2008 Meeting Papers 295, Society for Economic Dynamics.
    20. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.

    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:cfi:fseres:cf440. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/catokjp.html .

    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.