Insurance Products Ratemaking and Insurance Company Financial Solvency Ratio Calculation via Potential Deviation Ratio Method

Document Type : Research Paper


1 Associate Prof., Department of Financial Management and Insurance, Faculty of Management, University of Tehran, Tehran, Iran

2 Associate Prof., Department of Insurance, ECO College of Insurance, University of Allameh Tabataba'i, Tehran, Iran

3 Ph.D. Candidate, Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran


Objective: The goal of this research is to calculate the amount which must be paid for a fair premium based on the principle of equity and the financial solvency ratio of an insurance company based on the principle of equivalence, via potential deviation ratio method as a new method. Methods: The aggregate loss variable has been derived from Severity and Frequency of the losses. In this method, first the actual statistical distributions of these variables are estimated and then the fair premium is calculated based on the principle of equity. Next, the amount of potential deviation ratio, which is required to increase the financial solvency margin of the insurance company, is calculated. The model for calculating the premium, as well as the more precise concept of financial solvency of the insurance company that is provided in this research, is based on scientific foundations and can be used as a new method for all insurance fields. Results: The results of this research show that the calculated amount of premiums and potential deviation ratio that is required to increase the financial solvency ratio of the insurance company, by estimating the actual distribution of frequency and severity of the claims compared with when these variables are assumed to be normal distributed, are different. The difference is especially important in the higher levels of confidence. Conclusion: It can be concluded that in the case of calculating premiums and potential deviations based on assuming the normal distribution for the data, the real financial solvency ratio would be different from the apparent calculated financial solvency ratio of the insurance company. Furthermore, lacking the ability to precisely price the premiums may cause the insurance company to quickly fall down to bankruptcy. 


Main Subjects

Antonio, K., Valdez, E. (2010). Statistical concepts of a priori and a posteriori risk classification in insurance, UvA-DARE (Digital Academic Repository), Universiteit van Amsterdam, Electronic copy available at:
Aziz Nasiri, S., Gharakhani, M.,  Majedi, Z., Nasiri, F., Calculation of the solvency ratio of insurance companies based on the risk-based capital NAIC, Insurance World Updates, Insurance Research Center, 165, 4-14 .(in Persian)
Aziz Nasiri, S., Nasiri, F. (2015). Calculation of Rates and Risk Factors in Collision and Comprehensive Insurance Using Generalized Linear Model, Student Statistics Journal (NEDA),13(2), 35-47. (in Persian)
Bahnemann, D. (2015). Distributions for Actuaries, Copyright 2015, Casualty Actuarial Society.
Bajalan, S., Raei, R., Mohammadi, Sh. (2016). Modeling Insurance Claims Distribution through Combining Generalized Hyperbolic Skew-t Distribution with Extreme Value Theory. Financial Research Journal, 18(1), 39-58. (in Persian)
Bajalan, S., Raei, R., Mohammadi, Sh. (2017). Modeling Insurance Claim Distribution via Mixture Distribution and Copula. Financial Research Journal, 19(1), 23-40. (in Persian)
Bilandi, A. (2011).Computational Model of Insurance Institutions solvency ratio based on Accounting Approach, Insurance World Updates, Insurance Research Center, 162, 19-26.
(in Persian)
Chiappori, P. A., Jullien, B., Salanié, B., Salanié, F. (2006). Asymmetric Information in Insurance: General Testable Implications. RAND Journal of Economics, 37, 783-798.
Chiappori, P. A., Salanié, B. (2000). Testing for Asymmetric Information in Insurance Markets. Journal of Political Economy, 108(1), 56-78.
Denuit, M. (2006). An Actuarial Analysis of the French Bonus-Malus System. Scandinavian Actuarial Journal, 2006(5), 247-264.
Dionne, G., Gouriéroux, C., & Vanasse, C. (2001). Testing for Evidence of Adverse Selection in the Automobile Insurance Market: a Comment. Journal of Political Economy 109, 444-453.
Dionne, G., Gouriéroux, C., & Vanasse, C. (2006). The Informational Content of Household Decisions with Applications to Insurance under Asymmetric Information. in Competitive Failures in Insurance Markets: Theory and Policy Implications, MIT Press, London, pp. 159-184.
Frees, E.W. (2010). Regression Modeling with Actuarial and Financial Applications. Cambridge University Press, Cambridge.
Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M. (2008). Modern Actuarial Risk Theory Using R, Springer-Verlag Berlin Heidelberg.
Lemaire, J. (1995). Bonus-malus Systems in Automobile Insurance. Kluwer Academic Publishers, Boston.
Mahdavi, Gh., Nasiri, F. (2012). Fundamental and Theoretical principles of Insurance. Insurance Research Center (Affiliated to the central Insurance of Iran). (in Persian)
McCullagh, P., Nelder, J.A. (1989). Generalized Linear Models. (2nd ed). Chapman and Hall, London.
Mehregan, M., Safari, H., Jafarzadeh, A. (2015). Performance assessment of branches of Iran Insurance Corporation using data envelopment analysis. Financial Research Journal, 17(2), 393-414. (in Persian)
Mihaela, D. (2015). A review of theoretical concepts and empirical literature of non-life insurance pricing. Procedia Economics and Finance, 20, 157 – 162.
Motiee, A., Esmaeelzadeh, A., Jahanshad, A. (2017), The Relationship between Financial Solvency and Financial Variables of Insurance Companies, Iranian journal of Insurance Research, Insurance Research Center, 32(1), 23-42. (in Persian)
Nemati, M., Kazemi, A. (2014). Ranking of insurance companies using multi attribute decision making methods. Financial Research Journal, 16(1), 163-180. (in Persian)
Pesonen, E. (1962). A Numerical Method of Finding a Suitable Bonus Scale. ASTIN Bulleti 2(1), 102-108.
Safari, A., Kamali Dolatabadi, M. (2012). Life Insurance Pricing: A Linear Regression Method, 19th National Conference and Fifth International Seminar on Insurance and Development, Tehran, Insurance Research Center (Affiliated to the central Insurance of Iran). (in Persian)
Savage, L.J. (1954). The Foundation of Statistics. Dover Publications, New York.
Torkestani, M.S., Ghorbani, M., Forootan, M. (2013). Using data mining techniques to calculate and predict the financial solvency ratio of insurance companies, Twentieth National Conference on Insurance and Development, Insurance Research Center. (in Persian)
Werner, G., Modlin, C. (2016), Basic RateMaking, Casualty Actuarial Society.
Wüthrich, V., Switzerland, R. (2017). Non-Life Insurance: Mathematics & Statistics Lecture Notes. Version December 21, 2017, M.V. Wüthrich, ETH Zurich.