IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v28y2024i2d10.1007_s00780-024-00529-1.html
   My bibliography  Save this article

Optimal consumption and investment with welfare constraints

Author

Listed:
  • Junkee Jeon

    (Kyung Hee University)

  • Minsuk Kwak

    (Hankuk University of Foreign Studies)

Abstract

This paper investigates an optimal consumption and investment problem of an economic agent who faces a welfare constraint: the agent does not accept her expected utility (continuation value) to fall below a certain fixed level regardless of the time and state. This optimisation problem involves an infinite number of constraints. Using a duality approach, we transform infinitely many constraints into a single constraint and define a dual problem, which becomes a two-dimensional singular control problem. The dual problem provides its associated Hamilton–Jacobi–Bellman (HJB) equation with a gradient constraint. Under a general class of utility functions, we obtain an explicit solution to the HJB equation and provide optimal strategies by establishing a duality theorem. As an example, we consider hyperbolic absolute risk aversion (HARA) utility which may incorporate a government subsidy or basic support, and provide its solutions and implications.

Suggested Citation

  • Junkee Jeon & Minsuk Kwak, 2024. "Optimal consumption and investment with welfare constraints," Finance and Stochastics, Springer, vol. 28(2), pages 391-451, April.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:2:d:10.1007_s00780-024-00529-1
    DOI: 10.1007/s00780-024-00529-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-024-00529-1
    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/s00780-024-00529-1?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. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. Shuoqing Deng & Xun Li & Huyên Pham & Xiang Yu, 2022. "Optimal consumption with reference to past spending maximum," Finance and Stochastics, Springer, vol. 26(2), pages 217-266, April.
    3. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    4. Kenneth Arrow & Partha Dasgupta & Lawrence Goulder & Gretchen Daily & Paul Ehrlich & Geoffrey Heal & Simon Levin & Karl-Göran Mäler & Stephen Schneider & David Starrett & Brian Walker, 2004. "Are We Consuming Too Much?," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 147-172, Summer.
    5. He, Hua & Pages, Henri F, 1993. "Labor Income, Borrowing Constraints, and Equilibrium Asset Prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(4), pages 663-696, October.
    6. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    7. Campbell, John Y. & Sigalov, Roman, 2022. "Portfolio choice with sustainable spending: A model of reaching for yield," Journal of Financial Economics, Elsevier, vol. 143(1), pages 188-206.
    8. Shuoqing Deng & Xun Li & Huyên Pham & Xiang Yu, 2022. "Optimal consumption with reference to past spending maximum," Post-Print hal-03947571, HAL.
    9. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    10. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    11. Bertola, Giuseppe, 1998. "Irreversible investment," Research in Economics, Elsevier, vol. 52(1), pages 3-37, March.
    12. Philip H. Dybvig, 1995. "Dusenberry's Ratcheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for any Decline in Standard of Living," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 287-313.
    13. Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
    14. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    15. Shuoqing Deng & Xun Li & Huyen Pham & Xiang Yu, 2020. "Optimal Consumption with Reference to Past Spending Maximum," Papers 2006.07223, arXiv.org, revised Mar 2022.
    16. Bae, Se Yung & Jeon, Junkee & Koo, Hyeng Keun & Park, Kyunghyun, 2020. "Social insurance for the elderly," Economic Modelling, Elsevier, vol. 91(C), pages 274-299.
    17. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    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. Junkee Jeon & Hyeng Keun Koo & Minsuk Kwak, 2024. "Human capital and portfolio choice: borrowing constraint and reversible retirement," Mathematics and Financial Economics, Springer, volume 18, number 5, February.

    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. Junkee Jeon & Kyunghyun Park, 2021. "Portfolio selection with drawdown constraint on consumption: a generalization model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 243-289, April.
    2. Jeon, Junkee & Koo, Hyeng Keun & Shin, Yong Hyun, 2018. "Portfolio selection with consumption ratcheting," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 153-182.
    3. Geonwoo Kim & Junkee Jeon, 2024. "Optimal Consumption and Investment with Income Adjustment and Borrowing Constraints," Mathematics, MDPI, vol. 12(22), pages 1-14, November.
    4. Li, Xun & Yu, Xiang & Zhang, Qinyi, 2023. "Optimal consumption and life insurance under shortfall aversion and a drawdown constraint," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 25-45.
    5. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.
    6. Zvi Bodie & Jérôme Detemple & Marcel Rindisbacher, 2009. "Life-Cycle Finance and the Design of Pension Plans," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 249-286, November.
    7. Geonwoo Kim & Junkee Jeon, 2024. "Dynamic Asset Allocation and Retirement Decision with Consumption Ratcheting and Effort Choice," Mathematics, MDPI, vol. 12(23), pages 1-18, December.
    8. Zvi Bodie & Jonathan Treussard & Paul S. Willen, 2007. "The theory of life-cycle saving and investing," Public Policy Discussion Paper 07-3, Federal Reserve Bank of Boston.
    9. Mingxin Guo & Zuo Quan Xu, 2024. "Stochastic optimal self-path-dependent control: A new type of variational inequality and its viscosity solution," Papers 2412.11383, arXiv.org.
    10. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    11. Junkee Jeon & Hyeng Keun Koo & Kyunghyun Park, 2018. "Optimal Insurance with Limited Commitment in a Finite Horizon," Papers 1812.11669, arXiv.org, revised Jan 2019.
    12. De Angelis, Tiziano & Ferrari, Giorgio, 2014. "A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4080-4119.
    13. Luis Alvarez, 2010. "Irreversible capital accumulation under interest rate uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 249-271, October.
    14. Zongxia Liang & Xiaodong Luo & Fengyi Yuan, 2023. "Consumption-investment decisions with endogenous reference point and drawdown constraint," Mathematics and Financial Economics, Springer, volume 17, number 6, February.
    15. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    16. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    17. Roche, Hervé & Tompaidis, Stathis & Yang, Chunyu, 2013. "Why does junior put all his eggs in one basket? A potential rational explanation for holding concentrated portfolios," Journal of Financial Economics, Elsevier, vol. 109(3), pages 775-796.
    18. Giorgio Ferrari & Hanwu Li & Frank Riedel, 2020. "A Knightian Irreversible Investment Problem," Papers 2003.14359, arXiv.org, revised Apr 2020.
    19. Nicholas Bloom & John Van Reenen, 2002. "Patents, Real Options and Firm Performance," Economic Journal, Royal Economic Society, vol. 112(478), pages 97-116, March.
    20. Schwartz, Eduardo S & Tebaldi, Claudio, 2004. "Illiquid Assets and Optimal Portfolio Choice," University of California at Los Angeles, Anderson Graduate School of Management qt7q65t12x, Anderson Graduate School of Management, UCLA.

    More about this item

    Keywords

    Consumption and investment; Welfare constraints; General utility; Singular control problem; Duality approach; Dynamic constraints;
    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

    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:spr:finsto:v:28:y:2024:i:2:d:10.1007_s00780-024-00529-1. 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.