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Consumption-portfolio choice with preferences for cash

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  • Kraft, Holger
  • Weiss, Farina

Abstract

This paper studies a consumption-portfolio problem where money enters the agent’s utility function. We solve the corresponding Hamilton–Jacobi–Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence. Our results are robust to introducing recursive utility.

Suggested Citation

  • Kraft, Holger & Weiss, Farina, 2019. "Consumption-portfolio choice with preferences for cash," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 40-59.
    • Handle: RePEc:eee:dyncon:v:98:y:2019:i:c:p:40-59
    DOI: 10.1016/j.jedc.2018.09.006
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    References listed on IDEAS

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    Cited by:

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    2. Wei-Bin Zhang, 2020. "Inflation And Growth With The Miu Approach And The Equation Of Exchange," Social Sciences and Education Research Review, Department of Communication, Journalism and Education Sciences, University of Craiova, vol. 7(1), pages 45-71, July.
    3. Pengfei Luo & Yong Ma, 2021. "Robustly dynamic tax evasion and consumption with preferences for cash," International Review of Finance, International Review of Finance Ltd., vol. 21(3), pages 1078-1088, September.
    4. Zhao, Hui & Wang, Suxin, 2022. "Optimal investment and benefit adjustment problem for a target benefit pension plan with Cobb-Douglas utility and Epstein-Zin recursive utility," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1166-1180.
    5. Luo, Pengfei & Lu, Ting & Song, DanDan, 2021. "Real options for an entrepreneur with preferences for liquidity," Economics Letters, Elsevier, vol. 204(C).
    6. Jia Yue & Ming-Hui Wang & Nan-Jing Huang, 2022. "Global Optimal Consumption–Portfolio Rules with Myopic Preferences and Loss Aversion," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1427-1455, December.

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    More about this item

    Keywords

    Consumption-portfolio choice; Money in the utility function; Stock demand; Stochastic control; Recursive utility;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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