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Some Ruin Problems for a Risk Process with Stochastic Interest

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  • Kam-Chuen Yuen
  • Guojing Wang

Abstract

As investment plays an increasingly important role in the insurance business, ruin analysis in the presence of stochastic interest (or stochastic return on investments) has become a key issue in modern risk theory, and the related results should be of interest to actuaries. Although the study of insurance risk models with stochastic interest has attracted a fair amount of attention in recent years, many significant ruin problems associated with these models remain to be investigated. In this paper we consider a risk process with stochastic interest in which the basic risk process is the classical risk process and the stochastic interest process (or the stochastic return-on-investmentgenerating process) is a compound Poisson process with positive drift. Within this framework, we first derive an integro-differential equation for the Gerber-Shiu expected discounted penalty function, and then obtain an exact solution to the equation. We also obtain closed-form expressions for the expected discounted penalty function in some special cases. Finally, we examine a lower bound for the ruin probability of the risk process.

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  • Kam-Chuen Yuen & Guojing Wang, 2005. "Some Ruin Problems for a Risk Process with Stochastic Interest," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(3), pages 129-142.
    • Handle: RePEc:taf:uaajxx:v:9:y:2005:i:3:p:129-142
    DOI: 10.1080/10920277.2005.10596215
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    Citations

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    Cited by:

    1. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    2. Yin, Chuancun & Wen, Yuzhen, 2013. "An extension of Paulsen–Gjessing’s risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 469-476.
    3. Liang, Zhibin & Yuen, Kam Chuen & Guo, Junyi, 2011. "Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 207-215, September.
    4. Yuen, Kam C. & Wang, Guojing & Wu, Rong, 2006. "On the renewal risk process with stochastic interest," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1496-1510, October.
    5. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.
    6. Yuen, Kam C. & Wang, Guojing & Li, Wai K., 2007. "The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 104-112, January.
    7. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    8. Chuancun Yin & Yuzhen Wen, 2013. "An extension of Paulsen-Gjessing's risk model with stochastic return on investments," Papers 1302.6757, arXiv.org.

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