IDEAS home Printed from https://ideas.repec.org/a/kap/apfinm/v28y2021i2d10.1007_s10690-020-09312-6.html
   My bibliography  Save this article

Risk-Sensitive Asset Management with Lognormal Interest Rates

Author

Listed:
  • Hiroaki Hata

    (Hitotsubashi University)

Abstract

Risk-sensitive asset management on both finite and infinite time horizons are treated on a market with a bank account and a risky stock. The risk-free interest rate is formulated as a geometric Brownian motion, and affects the return of the risky stock. The problems become standard risk-sensitive control problems. We derive the Hamilton–Jacobi–Bellman equations and study these solutions. Using solutions, we construct optimal strategies and optimal values.

Suggested Citation

  • Hiroaki Hata, 2021. "Risk-Sensitive Asset Management with Lognormal Interest Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 169-206, June.
    • Handle: RePEc:kap:apfinm:v:28:y:2021:i:2:d:10.1007_s10690-020-09312-6
    DOI: 10.1007/s10690-020-09312-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10690-020-09312-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10690-020-09312-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hideo Nagai, 2011. "Asymptotics of the probability of minimizing 'down-side' risk under partial information," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 789-803.
    2. Mark H. A. Davis & Sébastien Lleo, 2014. "Risk-Sensitive Asset Management," World Scientific Book Chapters, in: RISK-SENSITIVE INVESTMENT MANAGEMENT, chapter 2, pages 17-40, World Scientific Publishing Co. Pte. Ltd..
    3. W. H. Fleming & S. J. Sheu, 2000. "Risk‐Sensitive Control and an Optimal Investment Model," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 197-213, April.
    4. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    5. Mark Davis & Sebastien Lleo, 2011. "Jump-Diffusion Risk-Sensitive Asset Management II: Jump-Diffusion Factor Model," Papers 1102.5126, arXiv.org, revised Sep 2012.
    6. Watanabe, Yûsuke, 2013. "Asymptotic analysis for a downside risk minimization problem under partial information," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1046-1082.
    7. Hiroaki Hata & Yasunari Iida, 2006. "A risk-sensitive stochastic control approach to an optimal investment problem with partial information," Finance and Stochastics, Springer, vol. 10(3), pages 395-426, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hiroaki Hata & Nien-Lin Liu & Kazuhiro Yasuda, 2022. "Expressions of forward starting option price in Hull–White stochastic volatility model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 101-135, June.

    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. Jan Obłój & Thaleia Zariphopoulou, 2021. "In memoriam: Mark H. A. Davis and his contributions to mathematical finance," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1099-1110, October.
    2. Jun Sekine, 2012. "Long-term optimal portfolios with floor," Finance and Stochastics, Springer, vol. 16(3), pages 369-401, July.
    3. Tadashi Hayashi & Jun Sekine, 2011. "Risk-sensitive Portfolio Optimization with Two-factor Having a Memory Effect," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(4), pages 385-403, November.
    4. Hideo Nagai, 2011. "Asymptotics of the probability of minimizing 'down-side' risk under partial information," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 789-803.
    5. Vladimir Cherny & Jan Obloj, 2013. "Optimal portfolios of a long-term investor with floor or drawdown constraints," Papers 1305.6831, arXiv.org.
    6. Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.
    7. Dariusz Zawisza, 2020. "On the parabolic equation for portfolio problems," Papers 2003.13317, arXiv.org, revised Oct 2020.
    8. Mark H.A. Davis & Sébastien Lleo, 2021. "Risk‐sensitive benchmarked asset management with expert forecasts," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1162-1189, October.
    9. Scott Robertson & Hao Xing, 2014. "Long Term Optimal Investment in Matrix Valued Factor Models," Papers 1408.7010, arXiv.org.
    10. Marcin Pitera & {L}ukasz Stettner, 2022. "Discrete-time risk sensitive portfolio optimization with proportional transaction costs," Papers 2201.02828, arXiv.org.
    11. Robertson, Scott & Xing, Hao, 2015. "Large time behavior of solutions to semi-linear equations with quadratic growth in the gradient," LSE Research Online Documents on Economics 60578, London School of Economics and Political Science, LSE Library.
    12. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    13. Aleksandr G. Alekseev & Mikhail V. Sokolov, 2016. "Benchmark-based evaluation of portfolio performance: a characterization," Annals of Finance, Springer, vol. 12(3), pages 409-440, December.
    14. Shankar, Ravi & Goel, Mayank, 2024. "Risk-sensitive benchmarked portfolio optimization under non-linear market dynamics," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    15. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    16. Sebastien Lleo & Wolfgang Runggaldier, 2025. "Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem," Papers 2501.06275, arXiv.org.
    17. Rüdiger Frey & Abdelali Gabih & Ralf Wunderlich, 2012. "Portfolio Optimization Under Partial Information With Expert Opinions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-18.
    18. Huyên Pham, 2003. "A large deviations approach to optimal long term investment," Finance and Stochastics, Springer, vol. 7(2), pages 169-195.
    19. Akihiko Inoue & Yumiharu Nakano, 2005. "Optimal long term investment model with memory," Papers math/0506621, arXiv.org, revised May 2006.
    20. Traian A. Pirvu & Gordan Zitkovic, 2007. "Maximizing the Growth Rate under Risk Constraints," Papers 0706.0480, arXiv.org.

    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:kap:apfinm:v:28:y:2021:i:2:d:10.1007_s10690-020-09312-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.