﻿ 基于POT模型的地震再保险定价研究 The Study of Seismic Reinsurance Pricing Question Based on POT Model

Statistics and Application
Vol.06 No.03(2017), Article ID:21699,13 pages
10.12677/SA.2017.63037

The Study of Seismic Reinsurance Pricing Question Based on POT Model

Qianru Meng1, Qin Shang2, Zhe Wang1

1School of Mathematical Sciences, Dalian University of Technology, Dalian Liaoning

2Faculty of Management and Economics, Dalian University of Technology, Dalian Liaoning

Received: Jul. 22nd, 2017; accepted: Aug. 11th, 2017; published: Aug. 15th, 2017

ABSTRACT

China is one of the countries with serious natural disasters in the world. But as an effective means to manage catastrophe risk, reinsurance develops immaturely in our country. In this paper, we take earthquake catastrophe for example. Basing on the direct economic loss data of the earthquake which exceed the M4.5 class from 1996 to 2015, we use POT model and the distribution of GPD to calculate earthquake catastrophe risk and give the VAR under different levels of confidence. In the end, by using the definition and properties of compound Poisson distribution, we put forward a method to calculate the net premium under different deductible undertaken by the reinsurance company. The paper provides theory reference and data support for the study of catastrophe reinsurance pricing question in our country.

Keywords:POT Model, Threshold, Compound Poisson Distribution, Reinsurance

1大连理工大学，数学与科学学院，辽宁 大连

2大连理工大学，管理与经济学部，辽宁 大连

1. 引言

2016年“十三五”规划明确指出：“中国要加快建立巨灾保险制度，建立政府推动、市场运作、风险共担的多层次巨灾保险体系。”而在这之中，再保险市场的建立和完善无疑有着举足轻重的地位。

2. 基于GDP分布的POT模型

Pickands证明，当阈值时，超额分布可以用GDP来近似 [8] ：

3. 地震巨灾损失风险评估

3.1. 数据的获取与处理

3.2. 数据厚尾性检验

Figure 1. The histogram of the logarithmic direct economic loss of each earthquake

3.3. 阈值的选取

GPD参数估计是否准确取决于阈值选取的适当与否。本文综合运用以下两种方法对阈值进行选取。

3.3.1. Hill图法

Figure 2. Q-Q plot for exponential distribution

Figure 3. Density default

Figure 4. Hill plot

3.3.2. 超额均值函数图法

3.4. 广义帕累托模型的建立

Figure 5. Mean excess function graph

Figure 6. Generalized Pareto distribution fitting diagnostic map. (a) P-P graph (b) Q-Q graph (c) reproducing horizontal graph (d) histogram and density function estimation graph

Table 1. Generalized Pareto distribution parameter estimation table

3.5. VAR的测度

,

4. 地震巨灾再保险定价

Figure 7. Fitted graph of truncated distribution

Figure 8. Fitted graph of tail distribution

Figure 9. Residual plot

Figure 10. Fitted graph of residual

Table 2. Premium scale calculation results

5. 结论

The Study of Seismic Reinsurance Pricing Question Based on POT Model[J]. 统计学与应用, 2017, 06(03): 320-332. http://dx.doi.org/10.12677/SA.2017.63037

1. 1. 孙祁祥, 郑伟, 等. 中国巨灾风险管理:再保险角色[J]. 财贸经济, 2004(9): 3-10.

2. 2. Hosking, J.R. and Wallis, J.R. (1987) Paremeter and Quantile Estimation for Generalize Pareto Distribution. Techno-Metrics, 29, 339-349. https://doi.org/10.1080/00401706.1987.10488243

3. 3. Lai, L.-H. and Wu, P.-H. (2008) Estimating the Threshold Value and Loss Distribution: Rice Damaged by Typhoons in Taiwan. African Journal of Agricultural Research, 3, 818-824.

4. 4. Chi, Y. and Tan, K.S. (2010) Optimal Reinsurance under VaR and CVaR Risk Measures: A Simple Approach. ASTIN Bulletin, 41, 487-509.

5. 5. Balbás, A., Balbás, B. and Heras, A. (2009) Optimal Reinsurance with General Risk Measures. Insurance: Mathematics and Economics, 44, 374-384.

6. 6. De Alba, E., Zúñiga, J. and Ramírez Corzo, M.A. (2008) Measurement and Transfer of Catastrophic Risks: A Simulation Analysis. ASTIN Bulletin, 40, 547-568.

7. 7. 赵智红, 李兴绪. 非寿险中巨额损失数据的拟合与精算[J]. 数理统计与管理, 2010, 29(3): 336-347.

8. 8. Balkema, A. and Haan, D.L. (1974) Residual Life Time at Great Age. Ann Probab, 9, 792-804.

9. 9. 桂文林. POT模型中GPD厚尾性及金融风险测度[J]. 数量经济技术经济研究, 2010, 10(1): 107-118.

10. 10. 郝军章, 崔玉杰. 基于模型的巨灾风险度量与保险模式研究——以地震风险为例[J]. 数理统计与管理, 2015, 35(1): 132-141.

11. 11. Embrechts, P. and Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance. Springer-Verlag, London, 102-130. https://doi.org/10.1007/978-3-642-33483-2

12. 12. 肖海清, 孟生旺. 极值理论及其在巨灾再保险定价中的应用[J]. 数理统计与管理, 2013, 32(2): 240-246.

13. 13. 任婧, 张节松. 基于POT模型的巨灾损失分布拟合及风险度量[J]. 科技与管理, 2015, 17(1): 75-80.