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带常利率的二维风险模型的破产概率

张媛媛 王文胜

张媛媛, 王文胜. 带常利率的二维风险模型的破产概率[J]. 华东师范大学学报(自然科学版), 2013, (6): 22-31.
引用本文: 张媛媛, 王文胜. 带常利率的二维风险模型的破产概率[J]. 华东师范大学学报(自然科学版), 2013, (6): 22-31.
ZHANG Yuan-yuan, WANG Wen-sheng. Ruin probabilities of a bidimensional risk model with constant interest rate[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 22-31.
Citation: ZHANG Yuan-yuan, WANG Wen-sheng. Ruin probabilities of a bidimensional risk model with constant interest rate[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 22-31.

带常利率的二维风险模型的破产概率

详细信息
  • 中图分类号: O211

Ruin probabilities of a bidimensional risk model with constant interest rate

  • 摘要: 在二维框架下, 研究了两种类型的破产. 当索赔分布是重尾分布时, 对于这两种类型的破产, 分别得到了生存概率满足的积分-微分方程, 以及有限时间破产概率的明确的渐进表\linebreak 达式.
  • [1] {1} GAO S, LIU Z M. The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy[J]. Journal of Computational and Applied Mathematics, 2010, 233: 2181-2188.
    {2} WANG G J, WU R. The expected discounted penalty function for the perturbed compound Poisson risk process with constant interest[J]. Insurance: Mathematics and Economics, 2008, 42: 59-64.
    {3} PROTTER P. Stochastic Integration and Differential Equations: A New Approach[M]. Berlin: Springer, 1992.
    {4} TANG Q H. The finite-time ruin probability of the compound poisson model with constant interest force[J]. Journal of Applied Probability, 2005, 42: 608-619.
    {5} LIN Q M, WANG R M. Calculation of ruin probabilities under a renewal risk model with interest force[J]. Journal of East China Normal University: Natural Science Edition, 2005(1): 46-52.
    {6} AVRAM F, PALMOWSKI Z, PISTORIUS M. A two-dimensional ruin problem on the positive quadrant[J]. Insurance:Mathematics and Economics, 2008, 42: 227-234.
    {7} LI J H, LIU Z M, TANG Q H. On the ruin probabilities of a bidimensional perturbed risk model[J]. Insurance:Mathematics and Economics, 2007, 41: 185-195.
    {8} DANG L F, ZHU N, ZHANG H M. Survival probability for a two-dimensional risk model[J]. Insurance:Mathematics and Economics, 2009, 44: 491-496.
    {9} ZHANG Y Y, WANG W S. Ruin probabilities of a bidimensional risk model with investment [J]. Statistics and Probability Letters, 2012, 82: 130-138.
    {10} LIU X J, GAO Q W, WANG Y B. A note on a dependent risk model with constant interest rate[J]. Statistics and Probability Letters, 2012, 82: 707-712.
    {11} TANG Q H, WANG G J, YUEN K C. Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model[J]. Insurance:Mathematics and Economics, 2010, 46: 362-370.
    {12} WANG K Y, WANG Y B, GAO Q W. Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate[J]. Methodology and Computing in Applied Probability, 2013, 15: 109-124.
    {13} MAULIK K, RESNICK S. Characterizations and examples of hidden regular variation[J]. Extremes, 2004, 7: 31-67.
    {14} TANG Q H, TSITSIASHVILI G. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks[J]. Stochastic Processes and their Applications, 2003, 108: 299-325.
    {15} LIPTSER R S, SHIRYAYEV A N. Theory of Martingales[M]. Dordrecht: Kluwer Academic Publishers Group, 1989.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2013-01-01
  • 修回日期:  2013-04-01
  • 刊出日期:  2013-11-25

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