IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n312640.html

Portfolio Selection with Liability and Affine Interest Rate in the HARA Utility Framework

Author

Listed:
  • Hao Chang
  • Kai Chang
  • Ji-mei Lu

Abstract

This paper studied an asset and liability management problem with stochastic interest rate, where interest rate is assumed to be governed by an affine interest rate model, while liability process is driven by the drifted Brownian motion. The investors wish to look for an optimal investment strategy to maximize the expected utility of the terminal surplus under hyperbolic absolute risk aversion (HARA) utility function, which consists of power utility, exponential utility, and logarithm utility as special cases. By applying dynamic programming principle and Legendre transform, the explicit solutions for HARA utility are achieved successfully and some special cases are also discussed. Finally, a numerical example is provided to illustrate our results.

Suggested Citation

  • Hao Chang & Kai Chang & Ji-mei Lu, 2014. "Portfolio Selection with Liability and Affine Interest Rate in the HARA Utility Framework," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:312640
    DOI: 10.1155/2014/312640
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/312640
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/312640?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
    ---><---

    References listed on IDEAS

    as
    1. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2003. "Optimal investment strategies in the presence of a minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 189-207, August.
    2. Xie, Shuxiang & Li, Zhongfei & Wang, Shouyang, 2008. "Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 943-953, June.
    3. Gao, Jianwei, 2008. "Stochastic optimal control of DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1159-1164, June.
    4. Cox, John C. & Ingersoll Junior, Jonathan E. & Ross, Stephen A., 2007. "A theory of the term structure of interest rates," RAE - Revista de Administração de Empresas, FGV-EAESP Escola de Administração de Empresas de São Paulo (Brazil), vol. 47(2), April.
    5. Hao Chang & Xi-min Rong, 2013. "An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Grasselli, Martino, 2003. "A stability result for the HARA class with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 611-627, December.
    7. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2003. "Optimal investment strategies in the presence of a minimum guarantee," ULB Institutional Repository 2013/7598, ULB -- Universite Libre de Bruxelles.
    8. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    10. Hao Chang & Xi-min Rong, 2013. "An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    11. Markus Leippold & Fabio Trojani & Paolo Vanini, 2011. "Multiperiod mean-variance efficient portfolios with endogenous liabilities," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1535-1546.
    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. Hao Chang & Xi-min Rong, 2013. "An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Chang, Hao, 2015. "Dynamic mean–variance portfolio selection with liability and stochastic interest rate," Economic Modelling, Elsevier, vol. 51(C), pages 172-182.
    3. Chang Hao & Wang Chunfeng & Fang Zhenming, 2017. "Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework," Journal of Systems Science and Information, De Gruyter, vol. 5(3), pages 229-249, June.
    4. Yao, Haixiang & Li, Zhongfei & Li, Duan, 2016. "Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability," European Journal of Operational Research, Elsevier, vol. 252(3), pages 837-851.
    5. Yumo Zhang, 2023. "Utility maximization in a stochastic affine interest rate and CIR risk premium framework: a BSDE approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 97-128, June.
    6. Han, Nan-wei & Hung, Mao-wei, 2012. "Optimal asset allocation for DC pension plans under inflation," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 172-181.
    7. Charles I. Nkeki, 2017. "Optimal Investment And Optimal Additional Voluntary Contribution Rate Of A Dc Pension Fund In A Jump-Diffusion Environment," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 1-26, December.
    8. Chang, Hao & Chang, Kai, 2017. "Optimal consumption–investment strategy under the Vasicek model: HARA utility and Legendre transform," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 215-227.
    9. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2004. "Optimal risk management in defined benefit stochastic pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 489-503, June.
    10. Wang, Ning & Zhang, Yumo, 2025. "Robust asset-liability management games in a stochastic market with stochastic cash flows under HARA utility," Insurance: Mathematics and Economics, Elsevier, vol. 124(C).
    11. Han, Nan-Wei & Hung, Mao-Wei, 2015. "The investment management for a downside-protected equity-linked annuity under interest rate risk," Finance Research Letters, Elsevier, vol. 13(C), pages 113-124.
    12. Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.
    13. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.
    14. Tang, Mei-Ling & Chen, Son-Nan & Lai, Gene C. & Wu, Ting-Pin, 2018. "Asset allocation for a DC pension fund under stochastic interest rates and inflation-protected guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 87-104.
    15. Mei Choi Chiu & Hoi Ying Wong, 2014. "Optimal Investment for Insurers with the Extended CIR Interest Rate Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    16. Grant E. Muller & Peter J. Witbooi, 2014. "An Optimal Portfolio and Capital Management Strategy for Basel III Compliant Commercial Banks," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    17. Guan, Guohui & Liang, Zongxia, 2015. "Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 99-109.
    18. Ma, Qing-Ping, 2011. "On "optimal pension management in a stochastic framework" with exponential utility," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 61-69, July.
    19. Mei-Ling Tang & Ting-Pin Wu & Ming-Chin Hung, 2022. "Optimal Pension Fund Management with Foreign Investment in a Stochastic Environment," Mathematics, MDPI, vol. 10(14), pages 1-21, July.
    20. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:312640. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.