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Minimization of absolute ruin probability under negative correlation assumption

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  • Liang, Zongxia
  • Long, Mingsi

Abstract

In this paper we consider the problem of minimizing the absolute ruin probability of an insurance company. The managers of the company control investment amount and risk exposure to minimize the absolute ruin probability. A negative correlation between insurer’s liabilities and capital gains in financial market is introduced. Under this negative correlation assumption, the explicit forms of the solutions and optimal strategies to this problem for all different parameters are derived. We find that the solutions of this problem are S-shaped and the optimal strategies fail to be monotonic or continuous.

Suggested Citation

  • Liang, Zongxia & Long, Mingsi, 2015. "Minimization of absolute ruin probability under negative correlation assumption," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 247-258.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:247-258
    DOI: 10.1016/j.insmatheco.2015.10.003
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    References listed on IDEAS

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    1. Jerome L. Stein, 2012. "Stochastic Optimal Control and the U.S. Financial Debt Crisis," Springer Books, Springer, edition 127, number 978-1-4614-3079-7, February.
    2. Zou, Bin & Cadenillas, Abel, 2014. "Optimal investment and risk control policies for an insurer: Expected utility maximization," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 57-67.
    3. Hans Gerber & Hailiang Yang, 2007. "Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 159-169.
    4. 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.
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    Cited by:

    1. Hiroaki Hata & Kazuhiro Yasuda, 2024. "Expected Power Utility Maximization of Insurers," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 31(3), pages 543-577, September.

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    More about this item

    Keywords

    Absolute ruin probability; Optimal proportional reinsurance; Optimal investment; Negative correlation; HJB equation; IM13; IB91; IM52; IE53;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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