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Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factors

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  • Guo, Fenglong

Abstract

Ruin problems of continuous-time models with various dependence structures under risky investment are extensively studied in the literature. Those studies focus on dependence structures arising from insurance businesses themselves and pay few attentions to dependence between insurance risk and investment risk. This study considers a continuous-time Poisson risk model with insurance claims and investment return jumps shocked by common systematic risk factors. Systematic risk factors cause immediate jumps of investment returns but there are often random delays for insurers to settle incurred claims. The study further assumes that the arrival times of claims are delayed by a common random time to the ones of their corresponding investment return jumps. When claim sizes are heavy-tailed distributed, a uniform asymptotic estimate for ruin probabilities of the model is established and a numerical study is given to show the accuracy of the result. The result captures the effect of the dependence structures caused by systematic risk factors on the asymptotic behaviors of ruin probabilities and allows arbitrary dependence structures between claim sizes and their corresponding investment return jumps.

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  • Guo, Fenglong, 2022. "Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factors," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    • Handle: RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321007189
    DOI: 10.1016/j.amc.2021.126634
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    References listed on IDEAS

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    1. Li, Jinzhu, 2016. "Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 195-204.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Tang, Qihe & Wang, Guojing & Yuen, Kam C., 2010. "Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 362-370, April.
    4. Fenglong Guo & Dingcheng Wang & Jiangyan Peng, 2019. "Tail asymptotic of discounted aggregate claims with compound dependence under risky investment," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(4), pages 810-830, February.
    5. Dickson,David C. M., 2016. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9781107154605.
    6. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.
    7. Klüppelberg, Claudia & Kostadinova, Radostina, 2008. "Integrated insurance risk models with exponential Lévy investment," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 560-577, April.
    8. Yang, Haizhong & Sun, Suting, 2013. "Subexponentiality of the product of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2039-2044.
    9. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    10. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    11. Asimit, Alexandru V. & Jones, Bruce L., 2008. "Dependence and the asymptotic behavior of large claims reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 407-411, December.
    12. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, January.
    13. Yang, Haizhong & Li, Jinzhu, 2014. "Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 185-192.
    14. Fenglong Guo & Dingcheng Wang, 2013. "Uniform asymptotic estimates for ruin probabilities of renewal risk models with exponential Lévy process investment returns and dependent claims," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(3), pages 295-313, May.
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