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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.
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  • 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:

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  • 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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV
  • [1] M. Al-Smadi, Credit Risk, Macroeconomic and Bank Specific Factors, VDM Verlag Dr. M$ü$ller, 2011.
    [2] E. BaranoffT. Sager and T. Shively, A semiparametric stochastic spline model as a managerial tool for potential insolvency, Journal of Risk and Insurance, 67 (2000), 369-396.  doi: 10.2307/253834.
    [3] A. Best, Best's insolvency study-property/casualty insurers, Best's Review-Property/Casualty Insurance Edition, (1991), 16-23. 
    [4] J. Carson and R. Hoyt, Life insurer financial distress: Classification models and empirical evidence, Journal of Risk and Insurance, 62 (1995), 764-775.  doi: 10.2307/253595.
    [5] J. Cheng and M. Weiss, The fole of rbc, hurricane exposure, bond portfolio duration, and macroeconomic and industry-wide factors in property-liability insolvency prediction, Journal of Risk and Insurance, 79 (2012), 723-750. 
    [6] H. Chew and C. Lim, On regularisation parameter transformation of support vector machines, Journal of Industrial and Management Optimization, 5 (2009), 403-415.  doi: 10.3934/jimo.2009.5.403.
    [7] S. ChoJ. Kim and J. Bae, An integrative model with subject weight based on neural network learning for bankruptcy prediction, Expert Systems with Applications, 36 (2009), 403-410.  doi: 10.1016/j.eswa.2007.09.060.
    [8] J. CumminsM. Grace and R. Phillips, Regulatory solvency prediction in property-liability insurance: Risk-based capital, audit ratios, and cash flow simulation, Journal of Risk and Insurance, 66 (1999), 417-458.  doi: 10.2307/253555.
    [9] U. DellepianeM. MarcantonioE. Laghi and S. Renzi, Bankruptcy prediction using support vector machines and feature selection during the recent financial crisis, International Journal of Economics and Finance, 7 (2015), 182-194.  doi: 10.5539/ijef.v7n8p182.
    [10] A. DimitrasR. SlowinskiR. Susmaga and C. Zopounidis, Business failure using rough set, European Journal of Operational Research, 114 (1998), 263-280. 
    [11] P. Du Jardin, Predicting bankruptcy using neural networks and other classification methods: The influence of variable selection techniques on model accuracy, Neurocomputing, 73 (2010), 2047-2060.  doi: 10.1016/j.neucom.2009.11.034.
    [12] M. GraceS. Harrington and R. Klein, Risk-based captial and solvency screening in property-liability insurance: Hypothesis and empirical tests, Journal of Risk and Insurance, 65 (1998), 213-243. 
    [13] M. Grant and S. Boyd, Cvx: Matlab Software for Disciplined Programming, version 1.2, Technical report, http://cvxr.com/cvx 2010.
    [14] S. Hsiao and T. Whang, A study of financial insolvency prediction model for life insurers, Expert Systems with Applications, 36 (2009), 6100-6107.  doi: 10.1016/j.eswa.2008.07.024.
    [15] M. Kim and D. Kang, Ensemble with neural networks for bankruptcy prediction, Expert Systems with Applications, 37 (2010), 3373-3379.  doi: 10.1016/j.eswa.2009.10.012.
    [16] G. LanckrietN. CristianiniP. BartlettL. El Ghaoui and M. Jordan, Learning the kernel matrix with semi-definite programming, Journal of Machine Learning Research, 5 (2004), 27-72. 
    [17] S. Lee and J. Urrutia, Analysis and prediction of insolvency in the property-liability insurance industry: A comparison of logit and hazard models, Journal of Risk and Insurance, 63 (1996), 121-130.  doi: 10.2307/253520.
    [18] J. LuoS.-C. FangY. Bai and Z. Deng, Fuzzy quadratic surface support vector machine based on fisher discriminant analysis, Journal of Industrial and Management Optimization, 12 (2016), 357-373.  doi: 10.3934/jimo.2016.12.357.
    [19] J. MariaS. Sanch and B. Carlos, Prediction of insolvency in non-life insurance companies using support vector machines, genetic algorithms and simulated annealing, Fuzzy Economic Review, 9 (2004), 79-94. 
    [20] J. Min and Y. Lee, Bankrupty prediction using support vector machine with optimal choice of kernel function parameters, Expert Systems with Applications, 28 (2005), 603-614. 
    [21] S. MinJ. Lee and I. Han, Hybrid genetic algorithms and support vector machines for bankruptcy prediction, Expert Systems with Applications, 31 (2006), 652-660.  doi: 10.1016/j.eswa.2005.09.070.
    [22] S. Pottier and D. Sommer, Empirical evidence on the value of group-level financial information in insurer solvency surveillance, Risk Management and Insurance Review, 14 (2011), 73-88.  doi: 10.1111/j.1540-6296.2011.01195.x.
    [23] S. SanchoD. MarioJ. MariaP. Fernando and B. Carlos, Feature selection methods involving support vector machines for prediction of insolvency in non-life insurance companies, Intelligent Systems in Accouting, Finance and Management, 12 (2004), 261-281. 
    [24] K. Schittkowski, Optimal parameter selection in support vector machines, Journal of Industrial and Management Optimization, 1 (2005), 465-476.  doi: 10.3934/jimo.2005.1.465.
    [25] B. Scholkopf and A. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press, 2002.
    [26] K. ShinT. Lee and H. Kim, An application of support vector machines in bankruptcy prediction model, Expert Systems and Applications, 28 (2005), 127-135.  doi: 10.1016/j.eswa.2004.08.009.
    [27] N. Siddiqi, Credit Risk Scorecards: Developing and Implementing Intelligent Credit Scoring, John Wiley & Sons, 2015. doi: 10.1002/9781119201731.
    [28] Y. TianM. SunZ. DengJ. Luo and Y. Li, A new fuzzy set and non-kernel svm approach for mislabeled binary classification with applications, IEEE Transactions on Fuzzy Systems, 25 (2017), 1536-1545. 
    [29] V. Vapnik, Statistical Learning Theory, John Wiley & Sons, Inc., New York, 1998.
    [30] C. WuG. TzengY. Goo and W. Fang, A real-valued genetic algorithm to optimize the parameters of support vector machine for predicting bankruptcy, Expert Systems with Applications, 32 (2007), 397-408.  doi: 10.1016/j.eswa.2005.12.008.
    [31] C. XieC. Luo and X. Yu, Financial distress prediction based on svm and mda methods: The case of chinese listed companies, Quality & Quantity, 45 (2011), 671-686.  doi: 10.1007/s11135-010-9376-y.
    [32] Z. YangW. You and G. Ji, Using partial least squares and support vector machines for bankruptcy prediction, Expert Systems with Applications, 38 (2011), 8336-8342.  doi: 10.1016/j.eswa.2011.01.021.
    [33] L. Zhang and N. Nielson, Solvency analysis and prediction in property casualty insurance: Incorporating economic and market predictors, Journal of Risk and Insurance, 82 (2015), 97-124. 
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