Article Contents
Article Contents

# Predicting non-life insurer's insolvency using non-kernel fuzzy quadratic surface support vector machines

Tian's research has been supported by the Chinese National Science Foundation #11401485 and # 71331004. Yang's research has been supported by the Sichuan soft science research project #2017ZR0294.
• Due to the serious consequence caused by insurers' insolvency, how to accurately predict insolvency becomes a very important issue in this area. Many methods have been developed to do this task by using some firm-level financial information. In this paper, we propose a new approach which incorporates several macroeconomic factors in the model and applies feature selection to eliminate the bad effect of some unrelated variables. In this way, we can obtain a more comprehensive and accurate model. More importantly, our method is based on the state-of-the-art non-kernel fuzzy quadratic surface support vector machine (FQSSVM) model which not only performs superiorly in prediction, but also becomes very applicable to the users. Finally, we conduct some numerical experiments based on the real data of non-lifer insurers from USA to show the predictive power and efficiency of our proposed method compared with other benchmark methods. Specifically, in a reasonable computational time, FQSSVM has the most accurate prediction rate and least Type Ⅰ and Type Ⅱ errors.

Mathematics Subject Classification: 90B90, 90B50.

 Citation:

• Figure 1.  ROC curves for one test in case C1

Figure 2.  ROC curves for one test in case C2

Figure 3.  ROC curves for one test in case C3

Table 1.  The firm-level explanatory variables for non-life insurers

 Index Figure Index Ratio F1 Surplus R1 Net Premium / Surplus F2 Net Technical Reserves R2 Tech. Res. / Net Premium F3 Total Other Liabilities R3 Tech. Res. / Surplus F4 Total Liabilities R4 Liq. Assets / Tech. Res.+ Oth. Liabs F5 Total Investments R5 Combined Ratio F6 Total Other Assets R6 Expense Ratio F7 Total Assets R7 Loss Ratio F8 Gross Premium Written R8 Investment Yield F9 Net Premium Written R9 Pre-Tax Profitability F10 Net Premium Earned R10 Liq. Assets/Net Tech. Res. F11 Underwriting Expenses R11 Liq. Ast+Debts ced Co/Net Tech. Res.+Oth Liabs F12 Underwriting Result R12 Profit Bef. Tax / Net Prem. Written F13 Net Investment Income R13 Gross Premium/Surplus F14 Profit Before Tax R14 Change in Surplus F15 Syndicate Profit R15 Change in Technical Reserves F16 Profit After Tax R16 Change in Net Premiums Written F17 Profit After Names Expenses

Table 2.  A confusion matrix

 Observation Total Good Bad Prediction Good Correct goods (true negative) Type Ⅱ error (false negative) Goods predicted Prediction Bad Type Ⅰ error (false positive) Correct bads (true positive) Bads predicted Total Goods observed Bads observed Sample size

Table 3.  Overall accuracy results for different methods in various cases

 Case Methods ANN SVM MDA LRA SLR FQSSVM C1 0.816 0.861 0.828 0.831 0.833 0.865 C2 0.837 0.881 0.862 0.864 0.850 0.888 C3 0.862 0.903 0.840 0.848 0.851 0.915

Table 4.  Type Ⅰ errors for different methods in various cases

 Case Type Ⅰ error ANN SVM MDA LRA SLR FQSSVM C1 0.185 0.141 0.173 0.170 0.168 0.137 C2 0.165 0.121 0.139 0.137 0.151 0.115 C3 0.139 0.099 0.161 0.154 0.151 0.088

Table 5.  Type Ⅱ errors for different methods in various cases

 Case Type Ⅱ error ANN SVM MDA LRA SLR FQSSVM C1 0.174 0.117 0.159 0.155 0.153 0.108 C2 0.135 0.094 0.128 0.119 0.136 0.079 C3 0.127 0.068 0.146 0.130 0.128 0.047

Table 6.  AUC results for different methods in different comparisons

 Case Methods ANN SVM MDA LRA SLR FQSSVM C1 0.832 0.861 0.839 0.835 0.829 0.856 C2 0.834 0.873 0.841 0.853 0.862 0.887 C3 0.840 0.882 0.844 0.851 0.856 0.892

Table 7.  Computational times (in seconds) for different methods in different comparisons

 Case Methods ANN SVM MDA LRA SLR FQSSVM C1 201.6 347.9 37.17 40.05 213.8 110.3 C2 214.3 336.2 36.91 39.28 195.1 98.65 C3 196.8 329.5 36.85 39.44 187.6 91.41

Table 8.  Main pros and cons of different methods

 Method Pros Cons ANN handle nonlinear structure adaptability to environments resistance to noise pattern recognition black-box character difficult to interpret hard to analyze results parameters choice SVM handle nonlinear structure distribution-free good performance kernel function choice parameters choice computational times MDA easy to implement computational times can't handle nonlinear structure strong assumption on data LRA easy to implement computational times can't handle nonlinear structure strong assumption on data SLR easy to implement a proper subset of variables can't handle nonlinear structure strong assumption on data computational times FQSSVM handle nonlinear structure no need for kernel function distribution-free good performance good generalization dimension expansion
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