A nonparametric data mining approach for risk prediction in car insurance: a case study from the Montenegrin market

Figures & data

Table 1. Initial data-set metadata.

Role	Name	Type	Statistics	Range	Missing
Label	Avg Claim Costs	numeric	avg = 1,338.330 +/− 2,525.931	[100.000; 33,000.000]	0
Regular	Mid Region	integer	avg = 0.600 +/− 0.490	[0.000; 1.000]	0
Regular	North Region	integer	avg = 0.216 +/− 0.412	[0.000; 1.000]	0
Regular	Mid Age	integer	avg = 0.867 +/− 0.340	[0.000; 1.000]	0
Regular	Young	integer	avg = 0.083 +/− 0.276	[0.000; 1.000]	0
Regular	Male	integer	avg = 0.863 +/− 0.344	[0.000; 1.000]	0
Regular	Motorcycle	integer	avg = 0.010 +/− 0.101	[0.000; 1.000]	0
Regular	Car	integer	avg = 0.946 +/− 0.227	[0.000; 1.000]	0
Regular	Number of Claims	integer	avg = 1.081 +/− 0.305	[1.000; 3.000]	0
Regular	Years of Ownership Policy	integer	avg = 2.361 +/− 0.753	[1.000; 3.000]	0
Regular	Number of Insurance Cases	integer	avg = 1.122 +/− 0.422	[1.000; 5.000]	0

Source: Authors’ calculations.

Table 2. Support vector regression models and their predictive performance.

Clusters	SVM Parameter Set:	PerformanceVector
	(obtained from training set -70% of data)	(obtained from test set -30% of data)
Cl0	SVM.svm_type = nu-SVR	root_mean_squared_error: 82.195 +/− 0.000
	SVM.gamma = 1.0	absolute_error: 70.772 +/− 41.802
	SVM.C = 400.06000000000006	relative_error: 8.89% +/− 4.86%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.930
	SVM.nu = 0.6	root_relative_squared_error: 0.937
	SVM.epsilon = 1.0	prediction_average: 790.278 +/− 87.759
Cl1	SVM.svm_type = nu-SVR	root_mean_squared_error: 45.902 +/− 0.000
	SVM.gamma = 0.2008	absolute_error: 37.006 +/− 27.158
	SVM.C = 200.08	relative_error: 6.67% +/− 4.74%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.698
	SVM.nu = 0.5	root_relative_squared_error: 0.754
	SVM.epsilon = 0.001	prediction_average: 547.902 +/− 60.885
Cl2	SVM.svm_type = nu-SVR	root_mean_squared_error: 44.099 +/− 0.000
	SVM.gamma = 1.0	absolute_error: 35.720 +/− 25.861
	SVM.C = 600.04	relative_error: 10.53% +/− 7.81%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.939
	SVM.nu = 0.5	root_relative_squared_error: 0.958
	SVM.epsilon = 0.8002	prediction_average: 346.035 +/− 46.036
Cl3	SVM.svm_type = nu-SVR	root_mean_squared_error: 363.327 +/− 0.000
	SVM.gamma = 0.4006	absolute_error: 292.081 +/− 216.090
	SVM.C = 400.06000000000006	relative_error: 7.50% +/− 5.32%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.826
	SVM.nu = 0.5	root_relative_squared_error: 0.791
	SVM.epsilon = 0.2008	prediction_average: 3866.672 +/− 459.503
Cl4	SVM.svm_type = nu-SVR	root_mean_squared_error: 962.335 +/− 0.000
	SVM.gamma = 0.4006	absolute_error: 444.481 +/− 853.536
	SVM.C = 1000.0	relative_error: 5.57% +/− 10.04%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.450
	SVM.nu = 1.0	root_relative_squared_error: 0.640
	SVM.epsilon = 0.8002	prediction_average: 6357.550 +/− 1503.147
Cl5	SVM.svm_type = nu-SVR	root_mean_squared_error: 120.336 +/− 0.000
	SVM.gamma = 0.001	absolute_error: 108.077 +/− 52.916
	SVM.C = 400.06000000000006	relative_error: 9.52% +/− 4.42%
	SVM.kernel_type = rbf	normalised_absolute_error: 1.000
	SVM.nu = 0.7	root_relative_squared_error: 1.000
	SVM.epsilon = 0.8002	prediction_average: 1138.717 +/− 120.387
Cl6.0	SVM.svm_type = nu-SVR	root_mean_squared_error: 17.935 +/− 0.000
	SVM.gamma = 0.001	absolute_error: 14.932 +/− 9.935
	SVM.C = 800.0200000000001	relative_error: 11.86% +/− 8.84%
	SVM.kernel_type = rbf	normalised_absolute_error: 1.008
	SVM.nu = 0.6	root_relative_squared_error: 1.003
	SVM.epsilon = 0.6003999999999999	prediction_average: 132.211 +/− 17.874
Cl6.1	SVM.svm_type = nu-SVR	root_mean_squared_error: 11.003 +/− 0.000
	SVM.gamma = 1.0	absolute_error: 8.670 +/− 6.775
	SVM.C = 400.06000000000006	relative_error: 3.56% +/− 2.82%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.861
	SVM.nu = 1.0	root_relative_squared_error: 0.921
	SVM.epsilon = 0.6003999999999999	prediction_average: 245.318 +/− 11.946
Cl6.2	SVM.svm_type = nu-SVR	root_mean_squared_error: 12.673 +/− 0.000
	SVM.gamma = 1.0	absolute_error: 10.269 +/− 7.427
	SVM.C = 0.1	relative_error: 5.24% +/− 4.10%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.968
	SVM.nu = 0.6	root_relative_squared_error: 0.996
	SVM.epsilon = 0.001	prediction_average: 201.381 +/− 12.718
Cl7	SVM.svm_type = nu-SVR	root_mean_squared_error: 148.115 +/− 0.000
	SVM.gamma = 0.6003999999999999	absolute_error: 122.093 +/− 83.853
	SVM.C = 200.08	relative_error: 7.45% +/− 5.39%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.807
	SVM.nu = 0.5	root_relative_squared_error: 0.824
	SVM.epsilon = 0.8002	prediction_average: 1658.751 +/− 179.792
Cl8	SVM.svm_type = nu-SVR	root_mean_squared_error: 240.754 +/− 0.000
	SVM.gamma = 0.6003999999999999	absolute_error: 193.130 +/− 143.748
	SVM.C = 1,000.0	relative_error: 7.49% +/− 4.85%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.754
	SVM.nu = 0.5	root_relative_squared_error: 0.762
	SVM.epsilon = 0.8002	prediction_average: 2467.624 +/− 315.976
Cl9	SVM.svm_type = nu-SVR	root_mean_squared_error: 4,225.478 +/− 0.000
	SVM.gamma = 0.2008	absolute_error: 3,544.845 +/− 2299.725
	SVM.C = 1,000.0	relative_error: 14.00% +/− 5.94%
	SVM.kernel_type = rbf	normalised_absolute_error: 0.723
	SVM.nu = 0.8	root_relative_squared_error: 0.774
	SVM.epsilon = 0.001	prediction_average: 24103.856 +/− 5462.292

Source: Authors’ calculations.

Table 3. Results of support vector regression models for prediction of claim size.

	Avg Claim Costs per Cluster	No Dev <10%	% Dev <10%	No Dev <20%	% Dev <20%
Cluster 0: 295 items	792.120	179	61%	290	98%
Cluster 1: 472 items	549.469	374	79%	471	100%
Cluster 2: 561 items	345.604	268	48%	485	86%
Cluster 3: 133 items	3916.260	98	74%	127	95%
Cluster 4: 193 items	6227.533	162	84%	182	94%
Cluster 5: 225 items	1150.810	133	59%	225	100%
Cluster6.0: 246 items	135.546	117	48%	205	83%
Cluster 6.1: 229 items	246.330	224	98%	229	100%
Cluster 6.2: 294 items	201.628	258	88%	294	100%
Cluster 7: 192 items	1672.738	158	82%	189	98%
Cluster 8: 158 items	2437.068	124	78%	153	97%
Cluster 9: 23 items	22727.100	5	22%	17	74%
Total number of items: 3,021	1338.330	2100	69%	2,867	95%

Source: Authors’ calculations.

Table 4. Model of logistic regression for prediction of claim occurrence.

Weighting Coefficients
Bias (offset): 0.113
w[Years of Ownership Policy] = 2.575
w[Number of Insurance Cases] = −0.389
w[Mid Region] = −0.549
w[North Region] = −0.108
w[Mid Age] = −0.658
w[Young] = 0.113
w[Male] = −0.804
w[Motorcycle] = 0.093
w[Car] = −0.065
w[Buses] = −0.012
w[Special motor vehicles] = −0.005
w[Towing vehicles] = 0.067
w[Trailers] = −0.002
w[Trucks] = −0.046

Source: Authors’ calculations.

Table 5. Performance of logistic model for prediction of claim occurrence.

	True 1	True 0	Class Precision (%)
Pred. 1	596	47	92.69
Pred. 0	462	1080	70.04
Class Recall	56.33%	95.83%	Accuracy: 76.70

Source: Authors’ calculations.