IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v68y2008i1p159-179.html
   My bibliography  Save this article

An optimal investment strategy with maximal risk aversion and its ruin probability

Author

Listed:
  • Begoña Fernández
  • Daniel Hernández-Hernández
  • Ana Meda
  • Patricia Saavedra

Abstract

In this paper we study an optimal investment problem of an insurer when the company has the opportunity to invest in a risky asset using stochastic control techniques. A closed form solution is given when the risk preferences are exponential as well as an estimate of the ruin probability when the optimal strategy is used. Copyright Springer-Verlag 2008

Suggested Citation

  • Begoña Fernández & Daniel Hernández-Hernández & Ana Meda & Patricia Saavedra, 2008. "An optimal investment strategy with maximal risk aversion and its ruin probability," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 159-179, August.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:1:p:159-179
    DOI: 10.1007/s00186-007-0191-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-007-0191-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-007-0191-8?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. Guerra, Manuel & de Lourdes Centeno, Maria, 2008. "Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 529-539, April.
    2. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    3. Hipp, Christian & Plum, Michael, 2000. "Optimal investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 215-228, October.
    4. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    5. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    6. Wang, Nan, 2007. "Optimal investment for an insurer with exponential utility preference," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 77-84, January.
    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. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    2. Xu, Lin & Zhang, Liming & Yao, Dingjun, 2017. "Optimal investment and reinsurance for an insurer under Markov-modulated financial market," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 7-19.

    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. Zhou, Qing, 2009. "Optimal investment for an insurer in the Lévy market: The martingale approach," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1602-1607, July.
    2. Zhao, Hui & Rong, Ximin & Zhao, Yonggan, 2013. "Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 504-514.
    3. Badaoui, Mohamed & Fernández, Begoña, 2013. "An optimal investment strategy with maximal risk aversion and its ruin probability in the presence of stochastic volatility on investments," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 1-13.
    4. Mohamed Badaoui & Begoña Fernández & Anatoliy Swishchuk, 2018. "An Optimal Investment Strategy for Insurers in Incomplete Markets," Risks, MDPI, vol. 6(2), pages 1-23, April.
    5. Qianqian Zhou & Junyi Guo, 2020. "Optimal Control of Investment for an Insurer in Two Currency Markets," Papers 2006.02857, arXiv.org.
    6. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    7. Gu, Ailing & Guo, Xianping & Li, Zhongfei & Zeng, Yan, 2012. "Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 674-684.
    8. Alia, Ishak & Chighoub, Farid & Sohail, Ayesha, 2016. "A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 212-223.
    9. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
    10. Yi, Bo & Li, Zhongfei & Viens, Frederi G. & Zeng, Yan, 2013. "Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 601-614.
    11. Christensen, Bent Jesper & Parra-Alvarez, Juan Carlos & Serrano, Rafael, 2021. "Optimal control of investment, premium and deductible for a non-life insurance company," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 384-405.
    12. Xu, Lin & Zhang, Liming & Yao, Dingjun, 2017. "Optimal investment and reinsurance for an insurer under Markov-modulated financial market," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 7-19.
    13. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
    14. Nian Yao & Zhiming Yang, 2017. "Optimal excess-of-loss reinsurance and investment problem for an insurer with default risk under a stochastic volatility model," Papers 1704.08234, arXiv.org.
    15. Zhang, Xin-Li & Zhang, Ke-Cun & Yu, Xing-Jiang, 2009. "Optimal proportional reinsurance and investment with transaction costs, I: Maximizing the terminal wealth," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 473-478, June.
    16. Guan, Guohui & Liang, Zongxia, 2014. "Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 105-115.
    17. Jin, Zhuo & Yang, Hailiang & Yin, G., 2021. "A hybrid deep learning method for optimal insurance strategies: Algorithms and convergence analysis," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 262-275.
    18. Lihua Bai & Huayue Zhang, 2008. "Dynamic mean-variance problem with constrained risk control for the insurers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 181-205, August.
    19. Yan Tong & Tongling Lv & Yu Yan, 2023. "Optimal Investment and Reinsurance Policies in a Continuous-Time Model," Mathematics, MDPI, vol. 11(24), pages 1-20, December.
    20. Wang, Nan, 2007. "Optimal investment for an insurer with exponential utility preference," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 77-84, January.

    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:mathme:v:68:y:2008:i:1:p:159-179. 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.