谢佳益, 张志民. 障碍分红风险模型下的破产赤字折现密度函数的统计估计[J]. 应用概率统计, 2023, 39(2): 197-217. DOI: 10.3969/j.issn.1001-4268.2023.02.003
引用本文: 谢佳益, 张志民. 障碍分红风险模型下的破产赤字折现密度函数的统计估计[J]. 应用概率统计, 2023, 39(2): 197-217. DOI: 10.3969/j.issn.1001-4268.2023.02.003
XIE Jiayi, ZHANG Zhimin. Estimating the Discounted Density Function of the Deficit at Ruin in a Risk Model with Barrier Dividend Strategy[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(2): 197-217. DOI: 10.3969/j.issn.1001-4268.2023.02.003
Citation: XIE Jiayi, ZHANG Zhimin. Estimating the Discounted Density Function of the Deficit at Ruin in a Risk Model with Barrier Dividend Strategy[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(2): 197-217. DOI: 10.3969/j.issn.1001-4268.2023.02.003

障碍分红风险模型下的破产赤字折现密度函数的统计估计

Estimating the Discounted Density Function of the Deficit at Ruin in a Risk Model with Barrier Dividend Strategy

  • 摘要: 本文研究了带有障碍分红策略的复合泊松风险模型下的破产赤字折现密度函数的统计估计.在索赔次数过程的泊松强度和个人索赔大小的密度函数均未知的情况下,我们运用COS方法构造了估计值, 并且推导出了估计值的一致性. 此外,在样本量有限情况下, 我们提供的仿真结果验证了此统计估计方法的有效性.

     

    Abstract: In this paper, we study the statistical estimation of the discounted density function of the deficit at ruin in the compound Poisson model with barrier dividend strategy. When both the Poisson intensity for the claim number process and the density function for the individual claim sizes are unknown, we use the COS method to construct the estimator. Under a large sample setting, we derive consistency property of the estimator. We also provide simulation results to verify the effectiveness of this estimation method when the sample size is finite.

     

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