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Consumption–investment strategies with non-exponential discounting and logarithmic utility

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  • Zhao, Qian
  • Shen, Yang
  • Wei, Jiaqin

Abstract

In this paper, we revisit the consumption–investment problem with a general discount function and a logarithmic utility function in a non-Markovian framework. The coefficients in our model, including the interest rate, appreciation rate and volatility of the stock, are assumed to be adapted stochastic processes. Following Yong (2012a,b)’s method, we study an N-person differential game. We adopt a martingale method to solve an optimization problem of each player and characterize their optimal strategies and value functions in terms of the unique solutions of BSDEs. Then by taking limit, we show that a time-consistent equilibrium consumption–investment strategy of the original problem consists of a deterministic function and the ratio of the market price of risk to the volatility, and the corresponding equilibrium value function can be characterized by the unique solution of a family of BSDEs parameterized by a time variable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:238:y:2014:i:3:p:824-835
    DOI: 10.1016/j.ejor.2014.04.034
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    Cited by:

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    2. Zongxia Liang & Keyu Zhang, 2023. "Time-inconsistent mean field and n-agent games under relative performance criteria," Papers 2312.14437, arXiv.org.
    3. Yushi Hamaguchi, 2019. "Time-inconsistent consumption-investment problems in incomplete markets under general discount functions," Papers 1912.01281, arXiv.org, revised Mar 2021.
    4. Wang Chunfeng & Chang Hao & Fang Zhenming, 2017. "Optimal Consumption and Portfolio Decision with Heston’s SV Model Under HARA Utility Criterion," Journal of Systems Science and Information, De Gruyter, vol. 5(1), pages 21-33, February.
    5. Ishak Alia & Farid Chighoub & Nabil Khelfallah & Josep Vives, 2021. "Time-Consistent Investment and Consumption Strategies under a General Discount Function," JRFM, MDPI, vol. 14(2), pages 1-27, February.
    6. Alin OPREANA, 2015. "A New Perspective of Investment Modelling at the European Union Level," Expert Journal of Economics, Sprint Investify, vol. 3(2), pages 143-148.

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