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Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments

Author

Listed:
  • Jing Liu

    (School of Finance, Renmin University of China, 59 Zhongguancun Street, Haidian District, Beijing 100872, China)

  • Huan Zhang

    (Department of Mathematics, University of St. Thomas—Minnesota, 2115 Summit Avenue, St. Paul, MN 55105, USA
    Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA)

Abstract

Motivated by the EU Solvency II Directive, we study the one-year ruin probability of an insurer who makes investments and hence faces both insurance and financial risks. Over a time horizon of one year, the insurance risk is quantified as a nonnegative random variable X equal to the aggregate amount of claims, and the financial risk as a d -dimensional random vector Y consisting of stochastic discount factors of the d financial assets invested. To capture both heavy tails and asymptotic dependence of Y in an integrated manner, we assume that Y follows a standard multivariate regular variation (MRV) structure. As main results, we derive exact asymptotic estimates for the one-year ruin probability for the following cases: (i) X and Y are independent with X of Fréchet type; (ii) X and Y are independent with X of Gumbel type; (iii) X and Y jointly possess a standard MRV structure; (iv) X and Y jointly possess a nonstandard MRV structure.

Suggested Citation

  • Jing Liu & Huan Zhang, 2017. "Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments," Risks, MDPI, vol. 5(2), pages 1-11, May.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:2:p:28-:d:97825
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    References listed on IDEAS

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    Cited by:

    1. Andrius Grigutis & Jonas Šiaulys, 2020. "Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model," Mathematics, MDPI, vol. 8(2), pages 1-30, January.

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