IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v36y2019i1-4p37-55n1.html
   My bibliography  Save this article

Optimal retirement planning under partial information

Author

Listed:
  • Bäuerle Nicole

    (Institute of Stochastics, Karlsruhe Institute of Technology, 76128Karlsruhe, Germany)

  • Chen An

    (Institute of Insurance Science, University of Ulm, Helmholtzstr. 20, 89069Ulm, Germany)

Abstract

The present paper analyzes an optimal consumption and investment problem of a retiree with a constant relative risk aversion (CRRA) who faces parameter uncertainty about the financial market. We solve the optimization problem under partial information by making the market observationally complete and consequently applying the martingale method to obtain closed-form solutions to the optimal consumption and investment strategies. Further, we provide some comparative statics and numerical analyses to deeply understand the consumption and investment behavior under partial information. Bearing partial information has little impact on the optimal consumption level, but it makes retirees with an RRA smaller than one invest more riskily, while it makes retirees with an RRA larger than one invest more conservatively.

Suggested Citation

  • Bäuerle Nicole & Chen An, 2019. "Optimal retirement planning under partial information," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 37-55, December.
    • Handle: RePEc:bpj:strimo:v:36:y:2019:i:1-4:p:37-55:n:1
    DOI: 10.1515/strm-2018-0027
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/strm-2018-0027
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/strm-2018-0027?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. Dybvig, Philip H. & Liu, Hong, 2010. "Lifetime consumption and investment: Retirement and constrained borrowing," Journal of Economic Theory, Elsevier, vol. 145(3), pages 885-907, May.
    2. John Piggott & Emiliano A. Valdez & Bettina Detzel, 2005. "The Simple Analytics of a Pooled Annuity Fund," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(3), pages 497-520, September.
    3. Philip H. Dybvig & Hong Liu, 2011. "Verification Theorems for Models of Optimal Consumption and Investment with Retirement and Constrained Borrowing," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 620-635, November.
    4. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    5. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    6. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    7. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    8. Gennotte, Gerard, 1986. "Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    9. Farhi, Emmanuel & Panageas, Stavros, 2007. "Saving and investing for early retirement: A theoretical analysis," Journal of Financial Economics, Elsevier, vol. 83(1), pages 87-121, January.
    10. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    11. Cocco, João F. & Gomes, Francisco J., 2012. "Longevity risk, retirement savings, and financial innovation," Journal of Financial Economics, Elsevier, vol. 103(3), pages 507-529.
    12. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    13. Lubos Pastor & Pietro Veronesi, 2009. "Learning in Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 361-381, November.
    14. 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.
    15. Chen, An & Hieber, Peter & Klein, Jakob K., 2019. "Tonuity: A Novel Individual-Oriented Retirement Plan," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 5-30, January.
    16. Nicole Bäuerle & Stefanie Grether, 2017. "Extremal Behavior Of Long-Term Investors With Power Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-13, August.
    17. Nicole Bauerle & Stefanie Grether, 2017. "Extremal Behavior of Long-Term Investors with Power Utility," Papers 1703.04423, arXiv.org, revised Jun 2017.
    18. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.
    19. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    20. Michele Longo & Alessandra Mainini, 2016. "Learning And Portfolio Decisions For Crra Investors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-21, May.
    21. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252, June.
    22. Delong, Łukasz & Chen, An, 2016. "Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 342-352.
    23. Kyoung Jin Choi & Gyoocheol Shim, 2006. "Disutility, Optimal Retirement, And Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 443-467, April.
    24. Kyoung Jin Choi & Gyoocheol Shim & Yong Hyun Shin, 2008. "Optimal Portfolio, Consumption‐Leisure And Retirement Choice Problem With Ces Utility," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 445-472, July.
    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. Andrea Tolentino Herrera & José Gerardo De la Vega Meneses, 2020. "Responsabilidad Social Corporativa como la clave para las empresas exitosas," Revista de Investigación en Ciencias Contables y Administrativas, Universidad Michoacana de San Nicolás de Hidalgo, Facultad de Contaduría y Ciencias Administrativas, vol. 6(1), pages 116-129, December.
    2. Andrea Tolentino Herrera & José Gerardo De la Vega Meneses, 2020. "Responsabilidad Social Corporativa como la clave para las empresas exitosas," Revista de Investigación en Ciencias Contables y Administrativas, Universidad Michoacana de San Nicolás de Hidalgo, Facultad de Contaduría y Ciencias Administrativas, vol. 6(1), pages 116-129, December.
    3. Johnstone, David, 2022. "Accounting research and the significance test crisis," CRITICAL PERSPECTIVES ON ACCOUNTING, Elsevier, vol. 89(C).

    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. Chen, An & Hentschel, Felix & Steffensen, Mogens, 2021. "On retirement time decision making," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 107-129.
    2. Nicole Bauerle & An Chen, 2022. "Optimal investment under partial information and robust VaR-type constraint," Papers 2212.04394, arXiv.org, revised Sep 2023.
    3. Zhou Yang & Hyeng Keun Koo, 2018. "Optimal Consumption and Portfolio Selection with Early Retirement Option," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1378-1404, November.
    4. An Chen & Giorgio Ferrari & Shihao Zhu, 2023. "Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning," Papers 2312.02943, arXiv.org.
    5. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.
    6. Jessica A. Wachter, 2010. "Asset Allocation," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 175-206, December.
    7. Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "The value of knowing the market price of risk," Annals of Operations Research, Springer, vol. 299(1), pages 101-131, April.
    8. Giorgio Ferrari & Shihao Zhu, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Papers 2311.12169, arXiv.org.
    9. Chen, An & Ferrari, Giorgio & Zhu, Shihao, 2023. "Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning," Center for Mathematical Economics Working Papers 684, Center for Mathematical Economics, Bielefeld University.
    10. Wolfgang Putschögl & Jörn Sass, 2008. "Optimal consumption and investment under partial information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(2), pages 137-170, November.
    11. Chen, An & Rach, Manuel, 2019. "Options on tontines: An innovative way of combining tontines and annuities," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 182-192.
    12. Choi, Kyoung Jin & Jeon, Junkee & Koo, Hyeng Keun, 2022. "Intertemporal preference with loss aversion: Consumption and risk-attitude," Journal of Economic Theory, Elsevier, vol. 200(C).
    13. Chae, Jiwon & Jang, Bong-Gyu & Park, Seyoung, 2023. "Analytic approach for models of optimal retirement with disability risk," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 68-75.
    14. Junkee Jeon & Hyeng Keun Koo & Yong Hyun Shin & Zhou Yang, 2021. "An Integral Equation Representation for Optimal Retirement Strategies in Portfolio Selection Problem," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 885-914, October.
    15. Jang, Bong-Gyu & Park, Seyoung & Zhao, Huainan, 2020. "Optimal retirement with borrowing constraints and forced unemployment risk," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 25-39.
    16. Lee, Ho-Seok & Lim, Byung Hwa, 2023. "Personal bankruptcy and post-bankruptcy liquidity constraint," Journal of Banking & Finance, Elsevier, vol. 152(C).
    17. Chao Deng & Xizhi Su & Chao Zhou, 2020. "Relative wealth concerns with partial information and heterogeneous priors," Papers 2007.11781, arXiv.org.
    18. Ferrari, Giorgio & Zhu, Shihao, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Center for Mathematical Economics Working Papers 683, Center for Mathematical Economics, Bielefeld University.
    19. Michele Longo & Alessandra Mainini, 2016. "Learning And Portfolio Decisions For Crra Investors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-21, May.
    20. Bäuerle, Nicole & Mahayni, Antje, 2024. "Optimal investment in ambiguous financial markets with learning," European Journal of Operational Research, Elsevier, vol. 315(1), pages 393-410.

    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:bpj:strimo:v:36:y:2019:i:1-4:p:37-55:n: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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.