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

Ye Tian; Wei Yang; Gene Lai; Menghan Zhao

doi:10.3934/jimo.2018081

Article Contents

2019, Volume 15, Issue 2: 985-999. Doi: 10.3934/jimo.2018081

This issue Previous Article A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications Next Article

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

1.
School of Business Administration and Collaborative Innovation Center of Financial Security, Southwestern University of Finance and Economics, Chengdu 611130, China
2.
School of Insurance and Collaborative Innovation Center of Financial Security, Southwestern University of Finance and Economics, Chengdu 611130, China
3.
Department of Finance, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA
4.
School of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China

Received: October 31, 2017

Revised: December 31, 2017

Early access: June 2018

Published: January 2019

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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Abstract

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.

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Mathematics Subject Classification: 90B90, 90B50.

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Figure 1. ROC curves for one test in case C₁

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Figure 2. ROC curves for one test in case C₂

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Figure 3. ROC curves for one test in case C₃

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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

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Table 2. A confusion matrix

		Observation		Total
		Good	Bad	Total
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

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

Case	Methods
Case	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

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

Case	Type Ⅰ error
Case	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

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

Case	Type Ⅱ error
Case	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

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Table 6. AUC results for different methods in different comparisons

Case	Methods
Case	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

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

Case	Methods
Case	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

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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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