Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T14:08:18.230Z Has data issue: false hasContentIssue false
  • English
  • Français

Pricing insurance policies with offsetting relationship

Published online by Cambridge University Press:  17 September 2021

Hamza Hanbali Open the ORCID record for Hamza Hanbali [Opens in a new window]
Hamza Hanbali*
Affiliation:
Department of Econometrics and Business Statistics, Monash University, Clayton VIC 3800, Australia
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates the benefits of incorporating diversification effects into the pricing process of insurance policies from two different business lines. The paper shows that, for the same risk reduction, insurers pricing policies jointly can have a competitive advantage over those pricing them separately. However, the choice of competitiveness constrains the underwriting flexibility of joint pricers. The paper goes a step further by modelling explicitly the relationship between premiums and the number of customers in each line. Using the total collected premiums as a criterion to compare the competing strategies, the paper provides conditions for the optimal pricing decision based on policyholders’ sensitivity to price discounts. The results are illustrated for a portfolio of annuities and assurances. Further, using non-life data from the Brazilian insurance market, an empirical exploration shows that most pairs satisfy the condition for being priced jointly, even when pairwise correlations are high.

Keywords

Pricing decisionMultiple business linesCompetitivenessG22L10D81
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 2 , July 2022 , pp. 261 - 287
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acharya, V.V., Hasan, I. & Saunders, A. 2006. Should banks be diversified? Evidence from individual bank loan portfolios. The Journal of Business 79, 1355–1412.CrossRefGoogle Scholar
Asimit, V. & Boonen, T.J. 2018. Insurance with multiple insurers: A game-theoretic approach. European Journal of Operational Research 267, 778–790.CrossRefGoogle Scholar
Asmussen, S., Christensen, B.J. & ThØgersen, J. 2019. Nash equilibrium strategies for push-pull competition in a frictional non-life insurance market. Insurance: Mathematics and Economics 87, 92–100.Google Scholar
Bayraktar, E. & Young, V. 2007. Hedging life insurance with pure endowments. lnsurance: Mathematics and Economics 40, 435–444.Google Scholar
Bhargava, H.K. 2013. Mixed bundling of two independently valued goods. Management Science 59, 2170–2185.CrossRefGoogle Scholar
Boonen, T.J., De Waegenaere, A. & Norde, H. 2017. Redistribution of longevity risk: The effect of heterogeneous mortality beliefs. Insurance: Mathematics and Economics 72, 175–188.Google Scholar
Chen, Y., Cheung, K.C., Choi, H.M.C. & Yam, S.C.P. 2020. Evolutionary credibility risk premium. Insurance: Mathematics and Economics 93, 216–229.Google Scholar
Cox, S.H. & Lin, Y. 2007. Natural hedging of life and annuity mortality risks. North American Actuarial Journal 11, 1–15.CrossRefGoogle Scholar
Cummins, J.D., Harrington, S.E. & Klein, R.W. 1991. Cycles and crises in property/casualty insurance: A background discussion. In Cycles and Crises in Property/Casualty Insurance: Causes and Implications for Public Policy (pp. 232–255). National Association of Insurance Commissioners, Kansas City, MO edn.Google Scholar
Cummins, J.D. & Nye, D.J. 1981. Portfolio optimization models for property-liability insurance companies: An analysis and some extensions. Management Science 27, 365–492.CrossRefGoogle Scholar
de Figueiredo, R. J. P. & Rawley, E. 2011. Skill, luck, and the multiproduct firm: Evidence from hedge funds. Management Science 57, 1963–1978.CrossRefGoogle Scholar
Dhaene, J., Tsanakas, A., Valdez, E.A. & Vanduffel, S. 2012. Optimal capital allocation principles. The Journal of Risk and Insurance 79, 1–28.CrossRefGoogle Scholar
Doherty, N. & Garven, J. 1986. Price regulation in property-liability insurance: A contingent-claims approach. The Journal of Finance 41, 1031–1050.CrossRefGoogle Scholar
Dutang, C., Albrecher, H. & Loisel, S. 2013. Competition among non-life insurers under solvency constraints: A game-theoretic approach. European Journal of Operational Research 231, 702–711.CrossRefGoogle Scholar
Emms, P. 2011. Pricing general insurance in a reactive and competitive market. Journal of Computational and Applied Mathematics 236, 1314–1332.CrossRefGoogle Scholar
Emms, P. 2012. Equilibrium pricing of general insurance policies. North American Actuarial Journal 16, 323–349.CrossRefGoogle Scholar
GökgÜr, B. & Karabati, S. 2019. Dynamic and targeted bundle pricing of two independently valued products. European Journal of Operational Research 279, 184–198.CrossRefGoogle Scholar
GrÜndl, H., Post, T. & Schulze, N.R. 2006. To hedge or not to hedge: managing demographic risk in life insurance companies. The Journal of Risk and Insurance 73, 19–41.CrossRefGoogle Scholar
GrÜndl, H. & Schmeiser, H. 2007a. Capital allocation for insurance companies – What good IS IT? The Journal of Risk and Insurance 74, 303–317.CrossRefGoogle Scholar
GrÜndl, H. & Schmeiser, H. 2007b. Discussion of “capital allocation in insurance: Economic capital and the allocation of the default option value” by Michael Sherris and John van der Hoek. North American Actuarial Journal 11, 163–164.CrossRefGoogle Scholar
Ibragimov, R., Jaffee, D. & Walden, J. 2018. Equilibrium with monoline and multiline structures. Review of Finance 22, 595–632.Google Scholar
Jaffee, D. 2006. Monoline restrictions, with applications to mortgage insurance and title insurance. Review of Industrial Organization 108, 28–83.Google Scholar
Kaas, R., Goovaerts, M., Dhaene, J. & Denuit, M. 2008. Modern Actuarial Risk Theory Using R. Springer.CrossRefGoogle Scholar
Kahane, Y. 1977. Determination of the product mix and the business policy of an insurance company – a portfolio approach. Management Science 23, 1037–1148.CrossRefGoogle Scholar
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. & Shin, Y. 1992. Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54, 159–178.CrossRefGoogle Scholar
Leland, H.E. 2007. Financial synergies and the optimal scope of the firm: implications for mergers, spinoffs, and structured finance. The Journal of Finance 62, 765–807.CrossRefGoogle Scholar
Li, J. & Haberman, S. 2015. On the effectiveness of natural hedging for insurance companies and pension plans. lnsurance: Mathematics and Economics 61, 286–297.Google Scholar
Li, N. & Lee, R. 2005. Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography 42, 575–594.CrossRefGoogle ScholarPubMed
Luciano, E., Regis, L. & Vigna, E. 2017. Single- and cross-generation natural hedging of longevity and financial risk. The Journal of Risk and Insurance 84, 961–986.CrossRefGoogle Scholar
Meier, U. & Outreville, F. 2006. Business cycles in insurance and reinsurance: The case of France, Germany and Switzerland. The Journal of Risk Finance 7, 160–176.CrossRefGoogle Scholar
Meyers, G. 2003. The economics of capital allocation. The Casualty Actuarial Society Forum.Google Scholar
Myers, S.C. & Read, J.A. 2001. Capital allocation for insurance companies. The Journal of Risk and Insurance 68, 545–580.CrossRefGoogle Scholar
OECD 2004. Insurance supervision and regulation in Latin America: A comparative assessment. OECD report.Google Scholar
OECD 2020. Regulatory and supervisory framework for insurance intermediation. OECD report.Google Scholar
Pantelous, A.A. & Passalidou, E. 2017. Optimal strategies for a non-linear premium-reserve model in a competitive insurance market. Annals of Actuarial Science 11, 1–19.CrossRefGoogle Scholar
Phillips, R.D., Cummins, D.J. & Allen, F. 1998. Financial pricing of insurance in the multiple-line insurance company. The Journal of Risk and Insurance 65, 597–636.CrossRefGoogle Scholar
R Core Team 2020. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.Google Scholar
Sharpsteen, C. & Bracken, C. 2020. tikzDevice: R Graphics Output in LaTeX Format. R package version 0.12.3.1.Google Scholar
Sherris, M. & van der Hoek, J. 2006. Capital allocation in insurance: Economic capital and the allocation of the default option value. North American Actuarial Journal 10, 39–61.CrossRefGoogle Scholar
Suter, J., Duke, C., Harms, A., Joshi, A., Rzepecka, J., Lechardoy, L., Hausemer, P., Wilhelm, C., Dekeulenaer, F. & Lucica, E. 2017. Study on consumers’ decision making in insurance services: A behavioural economics prespective. Final report prepared by London Economics, Ipsos and VVA Europe on behalf of the European Commission.Google Scholar
Taylor, G.C. 1986. Underwriting strategy in a competitive insurance environment. Insurance: Mathematics and Economics 5, 59–77.Google Scholar
Trapletti, A. & Hornik, K. 2019. tseries: Time Series Analysis and Computational Finance. R package version 0.10-47.Google Scholar
Tsai, J., Wang, J. & Tzeng, L. 2010. On the optimal product mix in life insurance companies using conditional value at risk. lnsurance: Mathematics and Economics 46, 235–241.Google Scholar
Venezian, E. 1985. Ratemaking methods and profit cycles in property and liability insurance. The Journal of Risk and Insurance 52, 477–500.CrossRefGoogle Scholar
Wang, C.-W., Huang, H.-C. & Hong, D.-C. 2013. A feasible natural hedging strategy for insurance companies. Insurance: Mathematics and Economics 52, 532–541.Google Scholar
Wang, J., Huang, H., Yang, S. & Tsai, J. 2010. An optimal product mix for hedging longevity risk in life insurance companies: The immunization theory approach. The Journal of Risk and Insurance 77, 473–497.CrossRefGoogle Scholar
Zanjani, G. 2002. Pricing and capital allocation in catastrophe insurance. Journal of Financial Economics 65, 283–305.CrossRefGoogle Scholar
Zhu, N. & Bauer, D. 2014. A cautionary note on natural hedging of longevity risk. North American Actuarial Journal 18, 104–115.CrossRefGoogle Scholar
Zweifel, P. & Eisen, R. 2012. Insurance Economics. Springer.CrossRefGoogle Scholar