IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v77y2017icp133-142.html
   My bibliography  Save this article

Purchasing casualty insurance to avoid lifetime ruin

Author

Listed:
  • Young, Virginia R.

Abstract

We determine the optimal strategies for purchasing deductible insurance and for investing in a risky financial market in order to minimize the probability of lifetime ruin when an individual is subject to an insurable loss that occurs at a Poisson rate. We specialize to the case for which the casualty loss is constant and insurance is priced actuarially fairly. We learn that the optimal deductible strategy is for the individual to purchase no insurance when her wealth is below a so-called buy level. However, when wealth is greater than the buy level, the individual optimally purchases full insurance coverage.

Suggested Citation

  • Young, Virginia R., 2017. "Purchasing casualty insurance to avoid lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 133-142.
    • Handle: RePEc:eee:insuma:v:77:y:2017:i:c:p:133-142
    DOI: 10.1016/j.insmatheco.2017.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668717301907
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2017.09.005?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. Young, Virginia R. & Zhang, Yuchong, 2016. "Lifetime ruin under ambiguous hazard rate," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 125-134.
    2. Promislow, S.David & Young, Virginia R., 2005. "Unifying framework for optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 347-364, June.
    3. Moore, Kristen S. & Young, Virginia R., 2006. "Optimal insurance in a continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 47-68, August.
    4. Victor C. Pestien & William D. Sudderth, 1985. "Continuous-Time Red and Black: How to Control a Diffusion to a Goal," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 599-611, November.
    5. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    6. Wang, Ting & Young, Virginia R., 2012. "Maximizing the utility of consumption with commutable life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 352-369.
    7. S. David Promislow & Virginia Young, 2005. "Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(3), pages 110-128.
    8. Sid Browne, 1999. "Beating a moving target: Optimal portfolio strategies for outperforming a stochastic benchmark," Finance and Stochastics, Springer, vol. 3(3), pages 275-294.
    9. William D. Sudderth & Ananda Weerasinghe, 1989. "Controlling a Process to a Goal in Finite Time," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 400-409, August.
    10. Wang, Ting & Young, Virginia R., 2012. "Optimal commutable annuities to minimize the probability of lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 200-216.
    11. Virginia Young, 2004. "Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 106-126.
    12. Erhan Bayraktar & David Promislow & Virginia Young, 2014. "Purchasing Term Life Insurance to Reach a Bequest Goal while Consuming," Papers 1412.2262, arXiv.org, revised Feb 2016.
    13. Milevsky, Moshe Arye & Ho, Kwok & Robinson, Chris, 1997. "Asset Allocation via the Conditional First Exit Time or How to Avoid Outliving Your Money," Review of Quantitative Finance and Accounting, Springer, vol. 9(1), pages 53-70, July.
    14. Moshe Milevsky & Chris Robinson, 2000. "Self-Annuitization and Ruin in Retirement," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 112-124.
    15. Sid Browne, 1997. "Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 468-493, May.
    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. Liang, Xiaoqing & Young, Virginia R., 2018. "Minimizing the probability of ruin: Optimal per-loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 181-190.

    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. Bayraktar, Erhan & Young, Virginia R., 2007. "Minimizing the probability of lifetime ruin under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 196-221, July.
    2. Bayraktar, Erhan & Young, Virginia R., 2016. "Optimally investing to reach a bequest goal," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 1-10.
    3. Landriault, David & Li, Bin & Li, Danping & Li, Dongchen, 2016. "A pair of optimal reinsurance–investment strategies in the two-sided exit framework," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 284-294.
    4. Bayraktar, Erhan & Promislow, S. David & Young, Virginia R., 2014. "Purchasing life insurance to reach a bequest goal," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 204-216.
    5. Erhan Bayraktar & Asaf Cohen, 2015. "Risk Sensitive Control of the Lifetime Ruin Problem," Papers 1503.05769, arXiv.org, revised Jul 2016.
    6. Liang, Xiaoqing & Young, Virginia R., 2018. "Minimizing the probability of ruin: Optimal per-loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 181-190.
    7. Young, Virginia R. & Zhang, Yuchong, 2016. "Lifetime ruin under ambiguous hazard rate," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 125-134.
    8. Liang, Xiaoqing & Young, Virginia R., 2023. "Annuitizing at a bounded, absolutely continuous rate to minimize the probability of lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 80-96.
    9. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2016. "Minimizing the probability of lifetime drawdown under constant consumption," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 210-223.
    10. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2015. "Optimal Investment to Minimize the Probability of Drawdown," Papers 1506.00166, arXiv.org, revised Feb 2016.
    11. Yener, Haluk & Soybilgen, Barış & Stengos, Thanasis, 2020. "A general model for financial crises: An application to eurozone crisis," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 202-229.
    12. Bayraktar, Erhan & Young, Virginia R., 2009. "Minimizing the lifetime shortfall or shortfall at death," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 447-458, June.
    13. Erhan Bayraktar & Virginia Young, 2011. "Proving regularity of the minimal probability of ruin via a game of stopping and control," Finance and Stochastics, Springer, vol. 15(4), pages 785-818, December.
    14. Erhan Bayraktar & David Promislow & Virginia Young, 2014. "Purchasing Term Life Insurance to Reach a Bequest Goal while Consuming," Papers 1412.2262, arXiv.org, revised Feb 2016.
    15. Erhan Bayraktar & Yuchong Zhang, 2014. "Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion," Papers 1402.1809, arXiv.org, revised Nov 2014.
    16. Erhan Bayraktar & Virginia Young, 2007. "Correspondence between lifetime minimum wealth and utility of consumption," Finance and Stochastics, Springer, vol. 11(2), pages 213-236, April.
    17. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2015. "Minimizing the expected lifetime spent in drawdown under proportional consumption," Finance Research Letters, Elsevier, vol. 15(C), pages 106-114.
    18. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2006. "Optimal investment decisions with a liability: The case of defined benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 81-98, August.
    19. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.
    20. Stamos, Michael Z., 2008. "Optimal consumption and portfolio choice for pooled annuity funds," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 56-68, August.

    More about this item

    Keywords

    Compound Poisson process; Casualty loss; Consumption; Optimal investment; Stochastic control;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:eee:insuma:v:77:y:2017:i:c:p:133-142. 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/inca/505554 .

    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.