Designing an Optimal Collision Premium Model with Emphasis on the Effect of Macroeconomic Variables on the Demand Function

Document Type : Research Paper

Authors

1 1. Ph.D, Department of Industrial Management, Faculty of Economics, Management and Administrative Affairs, University of Semnan, Semnan, Iran

2 Assistant Prof, Department of Business Management, Faculty of Economics, Management and Administrative Affairs, University of Semnan, Semnan, Iran.

Abstract

Determining a fair premium is an essential issue for insurance companies. Many premium models are based on risk analysis and market behavior. Risk analysis is divided into Priori pricing and Posteriori pricing. These models use claim frequency and claim severity. Market behavior models include some variables affecting the demand function to determine premium. In contrast, insurance companies involve with uninsurable risks such as economic risks in collision insurance, and the insurance premium depends on the price of competitors, because there are competitive insurance environments. Therefore, it is essential to consider macroeconomic variables in the demand function. This study, for the first time, includes the insurance penetration in the demand function. To achieve the goal, the researcher has selected a private company active in the insurance industry for sampling. The method used was based on stochastic dynamic programming. The wealth equation of the insurance company is determined based on the Markov process, and the objective function of the model is a quadratic form. The Demand function is described as a function of macroeconomic parameters such as elasticity of demand, inflation rate, and insurance penetration. The optimal premium is calculated for different levels of market premium. The results show the average premium of the market becomes bigger, the optimal premium becomes lower.
JEL Classification: E21, B22, C61

Keywords

References

  1. احسانی‌فر، مریم (1391). برآورد تابع تقاضای بیمه بدنه اتومبیل در کل صنعت بیمه ایران. پایان‌نامه کارشناسی ارشد، دانشکده مدیریت اقتصاد و حسابداری، دانشگاه پیام نور، تهران.
  2. براد فورد، دیوید اف. (1998). اقتصاد بیمه اموال و مسئولیت. ترجمه رضا افقی و امیر یوسفیان پور (1393). تهران: انتشارات پژوهشکده بیمه.
  3. غفاری، هادی، یونسی، علی، حسین‌پور کاظمی، محمد و خدادادکاشی، فرهاد (1395). نرخ رشد بهینه مخارج دولت: تئوری کنترل بهینه پویا. پژوهش‌های رشد و توسعه اقتصادی، 6(23)، 145-163.
  4. وامبا، آچیم، ریس، رای (2008). اقتصاد خرد بیمه، ترجمه علی سوری (1390). تهران: انتشارات پژوهشکده بیمه وابسته به بیمه مرکزی جمهوری اسلامی ایران.
  5. Ahlgrim, K.C., & D’Arcy, S.P. (2012). The Effect of Deflation or High Inflation on the Insurance Industry. Casualty Actuarial Society, Canadian Institute of Actuaries and Society of Actuaries.
  6. Antonio, K., & Valdez, E. A. (2010). Statistical concepts of a priori and a posteriori risk classification. Amsterdam: University of Amsterdam, Electronic copy available at: http://ssrn.com/abstract=1665463.
  7. Asmussen, S., Christensen, B., & Thogerson, J. (2019). Nash Equilibrium Premium Strategies for Push-Pull Competition in a Frictional Non-Life Insurance Market. Insurance: Mathematics and Economics.
  8. Bailey, R.A., & Simon, L.R.J. (1960). Two Studies in Automobile Insurance Ratemaking. ASTIN Bulletin, 1(4), 192-217.
  9. Beenstock, M., Dickinson, G., & Khajuria, S. (1988). The Relationship between property-liability insurance penetration and income: An international analysis. The Journal of Risk and Insurance, 55, 259–272.
  10. Bertsekas, D. P. (2005). Dynamic programming and suboptimal control: A survey from ADP to MPC. European Journal of Control, 11(4), 310-334.
  11. Boonen, T.J., Pantelous, A.A., & Wu, R. (2018). Insurance: Non-Cooperative Dynamic Games for General Insurance Markets. Insurance: Mathematics and Economics.
  12. Boubaker, H., & Sghaier, N. )2012(. How Do the Infation Rate and the Interest Rate Affect the Non-Life Insurance Premiums January Bulletin trimestriel de l'Institut des actuaires français. Institut des actuaires français, Paris Vol. n°12(Juillet -Décembre): 87- 111.
  13. Bradford, D-F. (1998). The economics of property-casualty insurance (translators: Reza Ofoghi & Amir Yosefianpour (2014). Tehran: Publications of the Insurance Research Institute.
  14. Browne, M., Chung, J. W., & Frees, W. (2000). International property-liability insurance consumption. The Journal of Risk and Insurance, 67, 73–90.
  15. David, M. (2015). Auto insurance premium calculation using generalized linear models, Procedia Economics and Finance 20, 147 – 156.
  16. Denuit, M., & Lang, S. (2004). Nonlife Ratemaking with Bayesian GAM’s. Insurance: Mathematics and Economics, 35(3), 627-647.
  17. Denuit, M., Maréchal, X., Pitrebois, S., & Walhin, J. F. )2007(. Actuarial Modeling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Scales. Wiley, New York.
  18. Dionne, G., & Vanasse, C. (1989). A Generalization of Automobile Insurance Rating Models: the Negative Binomial Distribution with a Regression Component. ASTIN Bulletin, 19(2), 199-212.
  19. Dionne, G., Vanasse, C. (1992). Automobile Insurance Ratemaking in the Presence of Asymmetrical Information. Journal of Applied Econometrics, 7(2), 149-165.
  20. Dragos, S. L. (2014). Life and non-life insurance demand: the different effects of influence factors in emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja, 27(1), 169–180.
  21. Emms, P., & Haberman, S. (2005). Pricing general insurance using optimal control theory. ASTIN Bulletin, 35(2), 427–453.
  22. Emms, P., Haberman, S., & Savoulli, I. (2007). Optimal strategies for pricing general insurance.Insurance: Mathematics and Economics, 40(1), 15–34.
  23. Emms, P. (2008). A stochastic demand model for optimal pricing of non-life insurance policies. Mathematical Control Theory and Finance, Springer-Verlang Berlin Heidelberg, 113–136.
  24. Emms, P. (2011). Pricing general insurance in a reactive and competitive market. Journal of Computational and Applied Mathematics, 236(6), 1314–1332.
  25. Esho, N., Kirievsky, A., Ward, D., & Zurbruegg, R. (2004). Law and the determinants of property-casualty insurance. The Journal of Risk and Insurance, 71, 265–283.
  26. Gourieroux, C., & Jasiak, J. (2004(. Heterogeneous Model with Application to Car Insurance. Insurance: Mathematics and Economics, 34(2), 177-192.
  27. Haugen, K-K. (2016). Stochastic Dynamic Programming. ISBN printed edition (print on demand): 978-82-15-02670-1, ISBN electronic pdf-edition: 978-82-15-02671-8.
  28. Huang, H-H. , Shiu Y-M., & Wang C-P. (2013). Optimal insurance contract with stochastic background wealth. Scandinavian Actuarial Journal, 2, 119-13.
  29. Jacobson, D.H. (1974). A General result in stochastic Optimal Control of Nonlinear Discrete-Time Systems with Quadratic Performance Criteria. Journal of Mathematical Analysis and Applications, 47, 153-161.
  30. Kaas, R., Goovaerts, M., Dhaene, J., & Denuit, M. ) 2008(, Modern Actuarial Risk Theory Using R, Springer-Verlag Berlin Heidelberg.
  31. Kjosevski, J. (2012). The determinants of life insurance demand in central and southeastern Europe. International journal of Economics and Finance, 4(3), 237-247.
  32. Krivo, R. (2009). An Update to D’Arcy’s ‘A Strategy for Property-Liability Insurers in Inflationary Times’, Casualty Actuarial Society E-Forum.
  33. Lee, C-C. Chiu, Y-B. (2012). The impact of real income on insurance premiums: Evidence from panel data, International Review of Economics & Finance, 21(1), 246–260.
  34. Lee, C-C. , Chiu, Y-B., & Chang, C-H. (2013). Insurance demand and country risks: A nonlinear panel data analysis, Journal of International Money and Finance, 36, 68-85.
  35. Li, W., & Seng Tan, K., & Wei, P. (2020). Demand for non-life insurance under habit formation (2020). Insurance: Mathematics and Economics.
  36. Lowe, S., & Warren, R. (2010). Post-Recession Inflation: An Emerging Risk for P&C Insurers, Emphasis 3, 24-29.
  37. McClenahan, C.L. (2001). Ratemaking. 4th ed. Foundations of Casualty Actuarial Science, Casualty Actuarial Science.
  38. Mourdoukoutas, F., Boonen, T., & Koo, B Pantelous, A I. (2021). Pricing in a competitive stochastic insurance market. Insurance: Mathematics and Economics, 97, 44-56.
  39. Outreville, F. (1990). The economic significance of insurance markets in developing Countries.The Journal of Risk and Insurance, 57, 487–498.
  40. Pantelous, A.A., & Passalidou, E. (2013). Optimal premium pricing policy in a competitive insurance market environment. Annals of Actuarial Science, 7(2), 175–191.
  41. Pantelous, A.A., & Passalidou, E. (2015). Optimal premium pricing strategies for competitive general insurance markets. Applied Mathematics and Computation, 259, 858–874.
  42. Pantelous, A.A., & Passalidou, E. (2015). Optimal Premium Pricing Strategy of General insurance in a competitive market with quadratic criteria 16th ASMDA Conference Proceedings, 30 June–4 July, Piraeus, Greece.
  43. Pantelous, A.A., & Passalidou, E. (2016). Optimal strategies for a Non-linear premium-reserve model in a competitive insurance Market.Annals of Actuarial Science, 11(1), 1–19.
  44. Park, S. C., & Lemaire, J. (2011a). The impact of culture on the demand for non-life insurance. Insurance and Risk Management. Working paper presented at The Wharton School, University of Pennsylvania.
  45. Park, S. C., & Lemaire, J. (2011b). Culture matters: Long-term orientation and the demand for life insurance. Philadelphia, PA: Wharton School, University of Pennsylvania.
  46. Pinquet, J. (1997). Allowance for Cost of Claims in Bonus-Malus Systems. ASTIN Bulletin, 27(1), 33-57.
  47. Sherden, W. (1984). An analysis of the determinants of the demand for automobile insurance. Journal of Risk and Insurance, 51, 49–62.
  48. Taylor, G.C. (1986). Underwriting strategy in a competitive insurance environment. Insurance: Mathematics and Economics, 5(1), 59–77.
  49. Treerattanapun, A. (2011). The impact of culture on non-life insurance consumption. Paper presented at Wharton Research Scholars Project, The University of Pennsylvania.
  50. https://www.cbi.ir/Inflation/Inflation_FA.aspx

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History

  • Receive Date: 06 September 2021
  • Revise Date: 24 June 2022
  • Accept Date: 28 June 2022

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