Journal of Guangxi Normal University(Natural Science Edition) ›› 2016, Vol. 34 ›› Issue (3): 68-73.doi: 10.16088/j.issn.1001-6600.2016.03.010

Previous Articles     Next Articles

Asmussen’s Approach to Ruin Time of the Dependent Multi-typeRisk Processes in a Stochastic Environment

WEN Yuzhuo1, TANG Shengda2, DENG Guohe2   

  1. 1.College of Economics and Management, Guangxi Normal University, Guilin Guangxi 541004, China;
    2.College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541004, China
  • Received:2016-01-18 Online:2016-09-30 Published:2018-09-17

Abstract: In this paper, a dependent multi-type risk process with a PH claim distribution in a stochastic environment is proposed. Using Asmussen’s method, this risk process is transformed into stochastic fluid queues (SFQ). By the theory of the SFQ, the Laplace-stieltjes transform (LST) of the ruin time, the ultimate ruin, and the distribution of the deficit are obtained. Finally, a numerical example is given to illustrate the theoretical results.

Key words: risk theory, ruin time, stochastic fluid queue, dependent multiple-type insurance

CLC Number: 

  • O211.9
[1] 崔宗宝, 金燕生, 王汉芹. 具有退保事件的多险种复合Poisson风险模型[J]. 辽宁工程技术大学学报(自然科学版), 2013,32(3): 425-428.
[2] 李碧云, 余国胜. 多险种多复合Poisson-Geometric过程的常利率风险模型[J]. 湖北大学学报(自然科学版), 2015, 37(3): 208-212.
[3] 牛银菊, 邓丽, 马崇武. 常利率下带投资的多险种风险模型的破产概率[J]. 江西师范大学学报(自然科学版), 2015, 39(3): 286-289. DOI:10.16357/j.cnki.issn1000-5862.2015.03.12.
[4] 乔克林,侯致武,李萍.常利率下特殊双险种风险模型的破产赤字[J].数学杂志,2013,33(3):552-558. DOI:10.13548/j.sxzz.2013.03.002.
[5] 张超权, 刘晓辉. 求解 MArP 风险过程破产时间的新方法[J]. 统计与决策, 2015 (21): 20-23. DOI:10.13546/j.cnki.tjyjc.2015.21.005.
[6] ASMUSSEN S,KOOLE G.Marked point processes as limits of Markovian arrival streams[J]. Journal of Applied Probability, 1993, 30(2): 365-372. DOI:10.2307/3214845.
[7] GERBER H U,SHIU E S W.The time value of ruin in a Sparre Andersen model [J].North American Actuarial Journal,2005, 9(2): 49-69. DOI:10.1080/10920277.2005.10596197.
[8] LI Shuanming,GARRIDO J.On a general class of renewal risk process: analysis of the Gerber-Shiu function[J]. Advances in Applied Probability, 2005, 37(3): 836-856.
[9] DICKSON D, DREKIC S.The joint distribution of the surplus prior to ruin and the deficit at ruin in some Sparre Andersen models [J]. Insurance: Mathematics and Economics, 2004, 34(1): 97-107. DOI:10.1016/j.insmatheco.2003.11.003.
[10] ASMUSSEN S.Stationary distributions via first passage times[M]//DSHALALOW J H.Advances in Queueing: Theory, Methods, and Open Problems.Boca Raton,FL:CRC Press,1995:79-102.
[11] BADESCU A,BREUER L, da SILYA SOARES A, et al.Risk processes analyzed as fluid queues[J]. Scand Actuar J, 2005(2): 127-141. DOI:10.1080/03461230410000565.
[12] BADESCU A L,LANDRIAULT D.Applications of fluid flow matrix analytic methods in ruin theory:a review[J]. Rev R Acad Cien Serie A Mat, 2009,103(2): 353-372.DOI: 10.1007/BF03191912.
[13] RAMASWAMI V.Passage times in fluid models with application to risk processes[J].Methodol Comput Appl Probab,2006,8(4):497-515. DOI:10.1007/s11009-006-0426-9.
[14] AHN S,RAMASWAMI V.Efficient algorithms for transient analysis of stochastic fluid flow models[J]. J Appl Probab,2005,42(2):531-549.
[15] TANG Shengda,TAN Liansheng.Erlangian approximation to finite time probability of blocking time of multi-class OBS nodes [J]. Photonic Network Communications, 2015,30(2):167-177. DOI:10.1007/s11107-015-0508-0.
[1] WEN Yuzhuo, TANG Shengda, DENG Guohe. Analysis of the Ruin Time of Threshold Dividend Strategy Risk Model under Stochastic Environment [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 56-62.
[2] TANG Sheng-da, QIN Yong-song. Gerber-Shiu Function of MAP Risk Process Perturbedby Diffusion [J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(3): 23-27.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!