Modern claim frequency and claim severity models: An application to the Russian motor own damage insurance market

Figures & data

Table 1. The distribution of the number of losses

	0 losses	1 loss	More than 2 losses
Number of policies	2,933	567	149

Figure 1. The distribution of the average claims in the whole sample.

Table 2. Descriptive statistics of the independent variables

Name	Mean	SD	Median	Min	Max
Franchise	0.19	0.69	0.00	0.00	4.00
Gender	0.56	0.50	1.00	0.00	1.00
ClassN	5.15	2.87	4.00	1.00	10.0
Credit	0.12	0.33	0.00	0.00	1.00
CarAge	1.27	1.59	1.00	0.00	7.00
Experience	9.71	8.12	8.00	0.00	46.0
SumIns	704,247.9	455,854.6	575,870.0	130,000.0	3,800,000.0

Table 3. The percentage of statistically significant estimates at the 10% significance level (out of 1,000 samples)

Variable’s name	Hurdlemodel (zero component)	Hurdle model (count component)	GLM-Gamma distribution model
Driving experience	100.0%	94.1%	6.2%
Franchise	99.6%	15.3%	0.7%
Class	71.1%	0.0%	65.0%
Gender	0.4%	39.1%	7.7%
Credit	0.0%	0.0%	15.7%
SumInsured	0.5%	0.0%	not included
CarAge	9.8%	0.0%	0.3%

Note: The SumInsured variable was not included into the GLM-Gamma distribution model since the average claimed loss is directly related to the sum insured, thus, the inclusion of sum insured would result in a biased estimation.

Figure 2. The GLM-Gamma distribution model estimates (from 1,000 subsamples).

Notes: In the graphs, the estimates of the coefficients are given along the X-axis, while the p-values of their individual significance tests are given along the Y-axis. The dashed horizontal line depicts the 10% level of significance, while the solid vertical line depicts the mean value of the estimated coefficients.

Figure 3. The hurdle model estimates (from 1,000 subsamples).

Notes: In the graphs, the estimates of the coefficients are given along the X-axis, while the p-values of their individual significance tests are given along the Y-axis. “0” and “1” at the end of the variable names represent the zero and the count components of the hurdle model correspondingly. The dashed horizontal line depicts the 10% level of significance, while the solid vertical line depicts the mean value of the estimated coefficients.