IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1808.04608.html
   My bibliography  Save this paper

On the optimal investment-consumption and life insurance selection problem with an external stochastic factor

Author

Listed:
  • Rodwell Kufakunesu
  • Calisto Guambe

Abstract

In this paper, we study a stochastic optimal control problem with stochastic volatility. We prove the sufficient and necessary maximum principle for the proposed problem. Then we apply the results to solve an investment, consumption and life insurance problem with stochastic volatility, that is, we consider a wage earner investing in one risk-free asset and one risky asset described by a jump-diffusion process and has to decide concerning consumption and life insurance purchase. We assume that the life insurance for the wage earner is bought from a market composed of $M>1$ life insurance companies offering pairwise distinct life insurance contracts. The goal is to maximize the expected utilities derived from the consumption, the legacy in the case of a premature death and the investor's terminal wealth.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1808.04608
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1808.04608
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mousa, A.S. & Pinheiro, D. & Pinto, A.A., 2016. "Optimal life-insurance selection and purchase within a market of several life-insurance providers," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 133-141.
    2. Olivier Menoukeu Pamen, 2015. "Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 998-1031, December.
    3. 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.
    4. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    5. Huaxiong Huang & Moshe A. Milevsky & Jin Wang, 2008. "Portfolio Choice and Life Insurance: The CRRA Case," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(4), pages 847-872, December.
    6. Belkacem Berdjane & Serguei Pergamenshchikov, 2013. "Optimal consumption and investment for markets with random coefficients," Finance and Stochastics, Springer, vol. 17(2), pages 419-446, April.
    7. Olivier Menoukeu Pamen, 2017. "Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 373-410, November.
    8. 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.
    9. N. C. Framstad & B. Øksendal & A. Sulem, 2004. "Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 77-98, April.
    10. 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.
    11. Olivier Menoukeu-Pamen & Romuald Hervé Momeya, 2017. "A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 349-388, June.
    Full references (including those not matched with items on IDEAS)

    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, Shumin & Luo, Dan & Yao, Haixiang, 2024. "Optimal investor life cycle decisions with time-inconsistent preferences," Journal of Banking & Finance, Elsevier, vol. 161(C).
    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. Christoph Hambel & Holger Kraft & Lorenz S. Schendel & Mogens Steffensen, 2017. "Life Insurance Demand Under Health Shock Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1171-1202, December.
    4. Rodwell Kufakunesu & Calisto Guambe, 2018. "Optimal investment-consumption and life insurance with capital constraints," Papers 1808.04613, arXiv.org.
    5. Calisto Guambe & Rodwell Kufakunesu, 2017. "Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach," Papers 1711.01760, arXiv.org.
    6. Wang, Hao & Siu, Tak Kuen & Hu, Shujie & Wang, Ning, 2024. "Life-cycle model with subsistence consumption constraint and state-dependent utilities," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    7. Kwak, Minsuk & Shin, Yong Hyun & Choi, U Jin, 2011. "Optimal investment and consumption decision of a family with life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 176-188, March.
    8. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Leibniz Institute for Financial Research SAFE.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Kraft, Holger & Schendel, Lorenz S. & Steffensen, Mogens, 2014. "Life insurance demand under health shock risk," SAFE Working Paper Series 40, Leibniz Institute for Financial Research SAFE.
    16. 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, January-A.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:1808.04608. 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.