IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v40y2018i2d10.1007_s00291-017-0502-2.html
   My bibliography  Save this article

Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions

Author

Listed:
  • Huiling Wu

    (Central University of Finance and Economics)

  • Chengguo Weng

    (University of Waterloo)

  • Yan Zeng

    (Sun Yat-sen University)

Abstract

This paper studies a multi-period investment–consumption optimization problem with a stochastic discount rate and a time-varying utility function, which are governed by a Markov-modulated regime switching model. The investment is dynamically reallocated between one risk-free asset and one risky asset. The problem is time inconsistent due to the stochastic discount rate. An analytical equilibrium solution is established by resorting to a game theoretical framework. Numerous sensitivity analyses and numerical examples are provided to demonstrate the effects of the stochastic discount rate and time-varying utility coefficients on the decision-maker’s investment–consumption behavior. Our results show that many properties which are satisfied in the classical models do not hold any more due to either the stochastic discount rate or the time-varying utility function.

Suggested Citation

  • Huiling Wu & Chengguo Weng & Yan Zeng, 2018. "Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(2), pages 541-582, March.
    • Handle: RePEc:spr:orspec:v:40:y:2018:i:2:d:10.1007_s00291-017-0502-2
    DOI: 10.1007/s00291-017-0502-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-017-0502-2
    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/s00291-017-0502-2?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. Weng, Chengguo, 2013. "Constant proportion portfolio insurance under a regime switching exponential Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 508-521.
    2. Pirvu, Traian A. & Zhang, Huayue, 2014. "Investment–consumption with regime-switching discount rates," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 142-150.
    3. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    4. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    5. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    6. Marín-Solano, Jesús & Navas, Jorge, 2009. "Non-constant discounting in finite horizon: The free terminal time case," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 666-675, March.
    7. Glenn W. Harrison & Morten I. Lau & Melonie B. Williams, 2002. "Estimating Individual Discount Rates in Denmark: A Field Experiment," American Economic Review, American Economic Association, vol. 92(5), pages 1606-1617, December.
    8. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    9. Hsiaw, Alice, 2013. "Goal-setting and self-control," Journal of Economic Theory, Elsevier, vol. 148(2), pages 601-626.
    10. Christopher Harris & David Laibson, 2013. "Instantaneous Gratification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 205-248.
    11. Zou, Ziran & Chen, Shou & Wedge, Lei, 2014. "Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 70-80.
    12. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    13. Çanakoglu, Ethem & Özekici, Süleyman, 2010. "Portfolio selection in stochastic markets with HARA utility functions," European Journal of Operational Research, Elsevier, vol. 201(2), pages 520-536, March.
    14. Zhongfei Li & Ken Seng Tan & Hailiang Yang, 2008. "Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(1), pages 47-64.
    15. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    16. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    17. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    18. repec:dau:papers:123456789/11473 is not listed on IDEAS
    19. Joao F. Cocco, 2005. "Consumption and Portfolio Choice over the Life Cycle," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 491-533.
    20. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    21. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    22. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    23. Wei, J. & Wong, K.C. & Yam, S.C.P. & Yung, S.P., 2013. "Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 281-291.
    24. Read, Daniel & Read, N. L., 2004. "Time discounting over the lifespan," Organizational Behavior and Human Decision Processes, Elsevier, vol. 94(1), pages 22-32, May.
    25. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(4), pages 1125-1152.
    26. Cheung, Ka Chun & Yang, Hailiang, 2004. "Asset Allocation with Regime-Switching: Discrete-Time Case," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 99-111, May.
    27. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    28. Wu, Huiling & Li, Zhongfei, 2012. "Multi-period mean–variance portfolio selection with regime switching and a stochastic cash flow," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 371-384.
    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. Escobar-Anel, Marcos & Gollart, Maximilian & Zagst, Rudi, 2022. "Closed-form portfolio optimization under GARCH models," Operations Research Perspectives, Elsevier, vol. 9(C).
    2. Weixuan Xia, 2023. "Optimal Consumption--Investment Problems under Time-Varying Incomplete Preferences," Papers 2312.00266, arXiv.org.

    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. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.
    2. Chen, Shumin & Luo, Dan & Yao, Haixiang, 2024. "Optimal investor life cycle decisions with time-inconsistent preferences," Journal of Banking & Finance, Elsevier, vol. 161(C).
    3. Koo, Ja Eun & Lim, Byung Hwa, 2021. "Consumption and life insurance decisions under hyperbolic discounting and taxation," Economic Modelling, Elsevier, vol. 94(C), pages 288-295.
    4. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    5. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    6. Zhao, Qian & Shen, Yang & Wei, Jiaqin, 2014. "Consumption–investment strategies with non-exponential discounting and logarithmic utility," European Journal of Operational Research, Elsevier, vol. 238(3), pages 824-835.
    7. Zou, Ziran & Chen, Shou & Wedge, Lei, 2014. "Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 70-80.
    8. Nicolas Drouhin, 2016. "Non stationary additive utility and time consistency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01238584, HAL.
    9. Liya Liu & Yingjie Niu & Yuanping Wang & Jinqiang Yang, 2020. "Optimal consumption with time-inconsistent preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 785-815, October.
    10. Chen, Shumin & Zeng, Yan & Hao, Zhifeng, 2017. "Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramér–Lundberg model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 31-45.
    11. Chen Shou & Xiang Shengpeng & He Hongbo, 2019. "Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-13, June.
    12. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    13. Kang, Myong-Il & Ikeda, Shinsuke, 2016. "Time discounting, present biases, and health-related behaviors: Evidence from Japan," Economics & Human Biology, Elsevier, vol. 21(C), pages 122-136.
    14. Richards, Timothy J. & Hamilton, Stephen F., 2012. "Obesity and Hyperbolic Discounting: An Experimental Analysis," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 37(2), pages 1-18, August.
    15. Bach Dong Xuan & Philippe Bich & Bertrand Wigniolle, 2022. "On multiple discount rates and present bias," Working Papers halshs-03884664, HAL.
    16. Caputo, Michael R., 2013. "The intrinsic comparative dynamics of infinite horizon optimal control problems with a time-varying discount rate and time-distance discounting," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 810-820.
    17. Lloyd-Smith, Patrick & Adamowicz, Wiktor & Entem, Alicia & Fenichel, Eli P. & Rouhi Rad, Mani, 2021. "The decade after tomorrow: Estimation of discount rates from realistic temporal decisions over long time horizons," Journal of Economic Behavior & Organization, Elsevier, vol. 183(C), pages 158-174.
    18. li, Hong & Mu, Congming & Yang, Jinqiang, 2016. "Optimal contract theory with time-inconsistent preferences," Economic Modelling, Elsevier, vol. 52(PB), pages 519-530.
    19. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    20. Zhao, Qian & Wang, Rongming & Wei, Jiaqin, 2016. "Exponential utility maximization for an insurer with time-inconsistent preferences," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 89-104.

    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:spr:orspec:v:40:y:2018:i:2:d:10.1007_s00291-017-0502-2. 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.