IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1711.01760.html
   My bibliography  Save this paper

Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach

Author

Listed:
  • Calisto Guambe
  • Rodwell Kufakunesu

Abstract

We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real money account and a risky share described by jump-diffusion processes. Using the theory of quadratic-exponential backward stochastic differential equation (BSDE) with jumps approach, we derive the optimal strategy for the two typical utilities (exponential and power) and the value function is characterized as a solution of BSDE with jumps. Finally, we derive the explicit solutions for the optimal investment in both cases of exponential and power utility functions for a diffusion case.

Suggested Citation

  • Calisto Guambe & Rodwell Kufakunesu, 2017. "Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach," Papers 1711.01760, arXiv.org.
    • Handle: RePEc:arx:papers:1711.01760
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1711.01760
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Morlais, Marie-Amelie, 2010. "A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1966-1995, September.
    2. Bernt Øksendal & Agnès Sulem, 2011. "Portfolio optimization under model uncertainty and BSDE games," Quantitative Finance, Taylor & Francis Journals, vol. 11(11), pages 1665-1674.
    3. Han, Nan-Wei & Hung, Mao-Wei, 2017. "Optimal consumption, portfolio, and life insurance policies under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 54-67.
    4. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    5. Bernt Oksendal & Agnès Sulem, 2011. "Portfolio optimization under model uncertainty and BSDE games," Working Papers inria-00570532, HAL.
    6. Guambe, Calisto & Kufakunesu, Rodwell, 2015. "A note on optimal investment–consumption–insurance in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 30-36.
    7. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
    8. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    9. Tiong, Serena, 2013. "Pricing inflation-linked variable annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 77-86.
    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. Calisto Guambe & Rodwell Kufakunesu & Gusti Van Zyl & Conrad Beyers, 2018. "Optimal asset allocation for a DC plan with partial information under inflation and mortality risks," Papers 1808.06337, arXiv.org, revised Aug 2018.

    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. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    2. Peng, Xingchun & Li, Baihui, 2023. "Optimal investment, consumption and life insurance purchase with learning about return predictability," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 70-95.
    3. Wei, Jiaqin & Cheng, Xiang & Jin, Zhuo & Wang, Hao, 2020. "Optimal consumption–investment and life-insurance purchase strategy for couples with correlated lifetimes," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 244-256.
    4. Rodwell Kufakunesu & Calisto Guambe, 2018. "On the optimal investment-consumption and life insurance selection problem with an external stochastic factor," Papers 1808.04608, arXiv.org.
    5. Chen, Chang-Chih & Chang, Chia-Chien & Sun, Edward W. & Yu, Min-Teh, 2022. "Optimal decision of dynamic wealth allocation with life insurance for mitigating health risk under market incompleteness," European Journal of Operational Research, Elsevier, vol. 300(2), pages 727-742.
    6. de Kort, J. & Vellekoop, M.H., 2017. "Existence of optimal consumption strategies in markets with longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 107-121.
    7. Jiang Cheng & Lu Yu, 2019. "Life and health insurance consumption in China: demographic and environmental risks," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(1), pages 67-101, January.
    8. Fujii, Masaaki & Takahashi, Akihiko, 2018. "Quadratic–exponential growth BSDEs with jumps and their Malliavin’s differentiability," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2083-2130.
    9. Masaaki Fujii & Akihiko Takahashi, 2016. "Quadratic-exponential growth BSDEs with Jumps and their Malliavin’s Differentiability (revised version of CARF-F-376)," CARF F-Series CARF-F-395, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Pirvu, Traian A. & Zhang, Huayue, 2012. "Optimal investment, consumption and life insurance under mean-reverting returns: The complete market solution," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 303-309.
    11. Madan, Dilip & Pistorius, Martijn & Stadje, Mitja, 2016. "Convergence of BSΔEs driven by random walks to BSDEs: The case of (in)finite activity jumps with general driver," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1553-1584.
    12. Chen, An & Hentschel, Felix & Klein, Jakob K., 2015. "A utility- and CPT-based comparison of life insurance contracts with guarantees," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 327-339.
    13. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    14. 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.
    15. Dirk Becherer & Martin Buttner & Klebert Kentia, 2016. "On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples," Papers 1607.06644, arXiv.org, revised Nov 2019.
    16. Arandjelović, Aleksandar & Kingston, Geoffrey & Shevchenko, Pavel V., 2023. "Life cycle insurance, bequest motives and annuity loads," Journal of Economic Dynamics and Control, Elsevier, vol. 157(C).
    17. Chen, Shumin & Luo, Dan & Yao, Haixiang, 2024. "Optimal investor life cycle decisions with time-inconsistent preferences," Journal of Banking & Finance, Elsevier, vol. 161(C).
    18. Erhan Bayraktar & Virginia Young, 2013. "Life Insurance Purchasing to Maximize Utility of Household Consumption," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(2), pages 114-135.
    19. de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge & Roch, Oriol, 2014. "Consumption, investment and life insurance strategies with heterogeneous discounting," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 66-75.
    20. Han, Nan-Wei & Hung, Mao-Wei, 2017. "Optimal consumption, portfolio, and life insurance policies under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 54-67.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1711.01760. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.