IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v284y2020i2p769-778.html
   My bibliography  Save this article

Simple explicit formula for near-optimal stochastic lifestyling

Author

Listed:
  • Černý, Aleš
  • Melicherčík, Igor

Abstract

In life-cycle economics, the Samuelson paradigm (Samuelson, 1969) states that the optimal investment is in constant proportions out of lifetime wealth composed of current savings and the present value of future income. It is well known that in the presence of credit constraints this paradigm no longer applies. Instead, optimal life-cycle investment gives rise to so-called stochastic lifestyling (Cairns, Blake, and Dowd, 2006), whereby for low levels of accumulated capital it is optimal to invest fully in stocks and then gradually switch to safer assets as the level of savings increases. In stochastic lifestyling not only does the ratio between risky and safe assets change but also the mix of risky assets varies over time. While the existing literature relies on complex numerical algorithms to quantify optimal lifestyling, the present paper provides a simple formula that captures the main essence of the lifestyling effect with remarkable accuracy.

Suggested Citation

  • Černý, Aleš & Melicherčík, Igor, 2020. "Simple explicit formula for near-optimal stochastic lifestyling," European Journal of Operational Research, Elsevier, vol. 284(2), pages 769-778.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:2:p:769-778
    DOI: 10.1016/j.ejor.2019.12.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719310720
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.12.032?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Vila, Jean-Luc & Zariphopoulou, Thaleia, 1997. "Optimal Consumption and Portfolio Choice with Borrowing Constraints," Journal of Economic Theory, Elsevier, vol. 77(2), pages 402-431, December.
    2. David B. Brown & James E. Smith, 2014. "Information Relaxations, Duality, and Convex Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 62(6), pages 1394-1415, December.
    3. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
    4. Joao F. Cocco, 2005. "Portfolio Choice in the Presence of Housing," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 535-567.
    5. Jianming Xia, 2008. "Risk Aversion and Portfolio Selection in a Continuous-Time Model," Papers 0805.0618, arXiv.org, revised Dec 2011.
    6. Aihua Zhang & Christian-Oliver Ewald, 2010. "Optimal investment for a pension fund under inflation risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 353-369, April.
    7. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    8. John M. Mulvey & Koray D. Simsek & Zhuojuan Zhang & Frank J. Fabozzi & William R. Pauling, 2008. "OR PRACTICE---Assisting Defined-Benefit Pension Plans," Operations Research, INFORMS, vol. 56(5), pages 1066-1078, October.
    9. Černý, Aleš & Miles, David & Schmidt, L'Ubomír, 2010. "The impact of changing demographics and pensions on the demand for housing and financial assets," Journal of Pension Economics and Finance, Cambridge University Press, vol. 9(3), pages 393-420, July.
    10. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    11. 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..
    12. ManMohan S. Sodhi, 2005. "LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications," Operations Research, INFORMS, vol. 53(2), pages 181-196, April.
    13. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    14. David B. Brown & James E. Smith & Peng Sun, 2010. "Information Relaxations and Duality in Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 785-801, August.
    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. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.

    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. Martin Haugh & Garud Iyengar & Chun Wang, 2016. "Tax-Aware Dynamic Asset Allocation," Operations Research, INFORMS, vol. 64(4), pages 849-866, August.
    2. Fabio C. Bagliano & Carolina Fugazza & Giovanna Nicodano, 2014. "Optimal Life-Cycle Portfolios for Heterogeneous Workers," Review of Finance, European Finance Association, vol. 18(6), pages 2283-2323.
    3. Paul Willen & Felix Kubler, 2006. "Collateralized Borrowing and Life-Cycle Portfolio Choice," NBER Working Papers 12309, National Bureau of Economic Research, Inc.
    4. Huiling Wu, 2016. "Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-17, July.
    5. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2016.
    6. Blake, David & Cairns, Andrew & Dowd, Kevin, 2008. "Turning pension plans into pension planes: What investment strategy designers of defined contribution pension plans can learn from commercial aircraft designers," MPRA Paper 33749, University Library of Munich, Germany.
    7. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 32, July-Dece.
    8. Robert Östling & Erik Lindqvist & David Cesarini & Joseph Briggs, 2016. "Wealth, Portfolio Allocations, and Risk Preference," 2016 Meeting Papers 1089, Society for Economic Dynamics.
    9. Horneff, Wolfram J. & Maurer, Raimond H. & Stamos, Michael Z., 2008. "Life-cycle asset allocation with annuity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3590-3612, November.
    10. repec:idb:brikps:365 is not listed on IDEAS
    11. Kihlstrom, Richard, 2009. "Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 634-663, September.
    12. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    13. Lai, Wan-Ni, 2016. "Do academic investment insights benefit society?," Research in International Business and Finance, Elsevier, vol. 38(C), pages 172-176.
    14. Briggs, Joseph & Cesarini, David & Lindqvist, Erik & Östling, Robert, 2021. "Windfall gains and stock market participation," Journal of Financial Economics, Elsevier, vol. 139(1), pages 57-83.
    15. Mei, Xiaoling & Nogales Martín, Francisco Javier, 2015. "Portfolio selection with proportional transaction costs and predictability," DES - Working Papers. Statistics and Econometrics. WS ws1521, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    17. Andreas Fagereng & Charles Gottlieb & Luigi Guiso, 2017. "Asset Market Participation and Portfolio Choice over the Life-Cycle," Journal of Finance, American Finance Association, vol. 72(2), pages 705-750, April.
    18. Calvet, Laurent E., 2001. "Incomplete Markets and Volatility," Journal of Economic Theory, Elsevier, vol. 98(2), pages 295-338, June.
    19. Rama Malladi, 2022. "HARI: Characteristics of a new defined lifestyle (DL) retirement planning product," Journal of Financial Services Marketing, Palgrave Macmillan, vol. 27(2), pages 147-163, June.
    20. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.
    21. Yueyang Zheng & Jingtao Shi, 2020. "A Stackelberg Game of Backward Stochastic Differential Equations with Applications," Dynamic Games and Applications, Springer, vol. 10(4), pages 968-992, December.

    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:eee:ejores:v:284:y:2020:i:2:p:769-778. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.