一类变保费双Cox风险模型的鞅分析

Abstract

Abstract:

This paper deals with a double Cox risk model of variable premium with investment income and reinsuranceU(t)=u+V1(t)=u1+u2+∑〖DD(〗M1(t)〖〗i=1〖DD)〗Xi-∑〖DD(〗M2(t)〖〗j=1〖DD)〗Zj+u2W(t).Using martingale obtained the expression of upper bound of the ultimate ruin probability -ru·C(r) on the assumption that M1(t) and M2(t) were correlated. And under special conditions M1(t)=β(t)M2(t), explicit upper bound of the ultimate ruin probability ψ(u)≤e-Ru was got, where R is Lundberg index.

Key words: Cox process, Brownian motion, martingale, stopping time; , Lundberg index

CLC Number:

O211.6

LEI Shu-Jiang, BAO Shu-Xin. Martingale Analysis on a Double Cox Risk Modelwith Variable Premium[J].J4, 2012, 50(03): 477-.

[1]	GAO Yufeng, FENG Decheng. Minimal Inequalities for Demi(sub)martingales#br# [J]. Journal of Jilin University Science Edition, 2018, 56(6): 1409-1413.
[2]	FENG Decheng, WANG Ying, LI Qinshe. A Class of Marshall Type Maximal Inequalities for Demimartingale [J]. Journal of Jilin University Science Edition, 2018, 56(4): 825-829.
[3]	JIA Xiuli, GUAN Lihong. Stability in Distribution of Stochastic VolterraLevinEquations Driven by Fractional Brownian Motion [J]. Journal of Jilin University Science Edition, 2017, 55(05): 1187-1191.
[4]	LIU Congmin, ZHANG Shuo, LI Qi, WANG Dehui. Risk Model with ChangePoint Claims Process [J]. Journal of Jilin University Science Edition, 2017, 55(03): 594-598.
[5]	GUAN Lihong, HAN Haiyan, ZHAO Yanan. A General Result on Precise Asymptotics for MovingAverage Process for Generation of Nonstationary Martingale Difference Sequences [J]. Journal of Jilin University Science Edition, 2016, 54(05): 1017-1021.
[6]	JIA Xiuli, GUAN Lihong, TANG Yu. Stochastic Maximum Principle for Stochastic Differential EquationsDriven by Fractional Brownian Motion with Jumps [J]. Journal of Jilin University Science Edition, 2016, 54(03): 521-523.
[7]	LI Gao-Meng, LI Hai-Feng. A Class of Riesz Decomposition for \|SetValued Submartingle [J]. J4, 2011, 49(06): 1039-1043.
[8]	REN Xiaohong, ZHANG Zhuokui, CHEN Huichan. Stochastic Integral of Local Square Strong Martingale [J]. J4, 2008, 46(05): 849-852.
[9]	LI Gaoming, ZHAO Hui. Riesz Approximation of Setvalued Martingale in the Limit and Its Convergence [J]. J4, 2007, 45(05): 713-716.
[10]	HU Hua. Theorems about Martingale Approximation andResolvent Representation Convergence [J]. J4, 2007, 45(05): 767-770.
[11]	CHEN Huichan, ZHANG Zhuokui, REN Xiaohong. Quadratic Variation of Local Square Strong Martingale [J]. J4, 2007, 45(05): 757-760.
[12]	ZHAO Hui, LI Gaoming. Riesz Decomposition of Setvalued L¹ Martingale in the Limit [J]. J4, 2006, 44(06): 916-918.
[13]	ZHANG Zhuokui, CHEN Huichan, REN Xiaohong. Stochastic Integral Based on Stopping Line [J]. J4, 2006, 44(05): 745-747.
[14]	ZHAO Hui, LI Gao-ming. Convergence and Riesz Decomposition of Set-valued Submartingale [J]. J4, 2006, 44(02): 181-184.
[15]	HAN Yu, YANG Xiao-yun, DONG Zhi-shan. A Functional Central Limit Theorem for the Random Sum of Linear Process of Martingale Differences [J]. J4, 2005, 43(06): 716-724.

Martingale Analysis on a Double Cox Risk Modelwith Variable Premium

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10