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Competition-Originated Cycles and Insurance Strategies

Published online by Cambridge University Press:  09 August 2013

Vsevolod K. Malinovskii
Vsevolod K. Malinovskii*
Affiliation:
Central Economics and Mathematics Institute (CEMI), 117418, Nakhimovskiy prosp., 47, Moscow, Russia, and Finance Academy, 125468, Leningradskiy prosp., 49, Moscow, Russia, E-Mail: [email protected], [email protected], URL: http://www.actlab.ru
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Abstract

An insurance company entering the property and liability insurance market at the high point of the insurance cycle may decide to slash premiums to gain an advantageous market share. Such aggressive intrusion may call forth a concerted industry response, producing a severe decline in the insurance market price. This can ruin some companies, and agrees with the observation that the insurance cycles are correlated with clustered insolvencies. This paper addresses a quantitative analysis of competition-originated cycles; it explores an interplay of rational aggressive and defensive strategies in the multi-period Lundberg-type controlled risk model.

Keywords

Underwriting cyclescompetitionyears of soft and hard marketmultiperiod insurance processsolvency and subsistence
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 797 - 843
Copyright
Copyright © International Actuarial Association 2010

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References

Asmussen, S. (1984; 1985) Approximations for the probability of ruin within finite time, Scandinavian Actuarial Journal, 64, 31–57.Google Scholar
Asmussen, S. (2000) Ruin Probabilities. World Scientific Publishers: Singapore.CrossRefGoogle Scholar
Asmussen, S. and Rolski, T. (1994) Risk theory in a periodic environment: the Cramér-Lundberg approximation and Lundbergs inequality. Math. Oper. Res., 19(2), 410–433.CrossRefGoogle Scholar
Best's Insolvency Study: Property/Casualty Insurers 1969-1990 (Oldwick, NJ: A.M. Best Company, June 1991).Google Scholar
Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer Verlag, New York.Google Scholar
Cummins, J.D. and Outreville, J.F. (1987) An international analysis of underwriting cycles in property-liability insurance, Journal of Risk and Insurance, June 1987, 246–262.CrossRefGoogle Scholar
Cummins, D., McGill, D., Winklevoss, H. and Zelten, H. (1974) Consumer Attitudes Toward Auto and Homeowners Insurance. Philadelphia, Pa.: Department of Insurance, Wharton School.Google Scholar
D'Arcy, S.P., Gorvett, R.W., Herbers, J.A., Hettinger, T.E., Lehmann, S.G. and Miller, M.J. (1997) Building a public access PC-based DFA model. CAS Forum, 1997.Google Scholar
Daykin, C.D., Pentikäinen, T. and Pesonen, M. (1996) Practical Risk Theory for Actuaries. Chapman and Hall, London, etc. Google Scholar
Doherty, N.A. and Garven, J.R. (1995) Insurance cycles: interest rates and the capacity constraint model. The Journal of Business, 68(3), 383–404.Google Scholar
Doherty, N.A. and Kang, H.B. (1988) Interest rates and insurance price cycles, Journal of Banking and Finance, 12(2), 199–214.Google Scholar
Feldblum, S. (2001) Underwriting cycles and business strategies, Proceedings of the Casualty Actuarial Society, LXXXVIII, 175–235.Google Scholar
Feldblum, S. (2007a) Underwriting cycles and insurance solvency. Casualty Actuarial Society Discussion Paper Program Casualty Actuarial Society – Arlington, Virginia 1992: May, Vol. 1, 383–438, http://www.casact.org/pubs/dpp/dpp92/92dpp383.pdf Google Scholar
Feldblum, S. (2007b) Underwriting cycles and ruin probability, Manuscript.Google Scholar
Gerber, H.U. and Shiu, E.S.W. (1997) The joined distribution of the time of ruin, the surplus immediately before ruin, and the dei cit at ruin, Insurance: Mathematics and Economics, 21, 129–137.Google Scholar
Gihman, I.I. and Skorokhod, A.V. (1979) Controlled Stochastic Processes. Springer-Verlag, New York etc. Google Scholar
Grandell, J. (1991) Aspects of Risk Theory. Springer-Verlag, New York etc. Google Scholar
Johnson, G. and Scholes, K. (1988) Exploring Corporate Strategy. Text and Cases (2nd edn). Prentice-Hall, Hemel Hempstead.Google Scholar
Joskow, P. (1973) Cartels, Competition and Regulation in the Property-Liability Insurance Industry, Bell Journal of Economics 4, 375–427.Google Scholar
Kaufmann, R., Gadmer, A. and Klatt, R. (2001) Introduction to dynamic financial analysis. RiskLab Switzerland, April 26, 2001.Google Scholar
Harrington, S.E. and Danzon, P.M. (1994) Pricing cutting in liability insurance markets, The Journal of Business, 67(4), 511–538.Google Scholar
Malinovskii, V.K. (1993) Limit theorems for stopped random sequences. I: rates of convergence and asymptotic expansions, Theory Probab. Appl., 38, 673–693.Google Scholar
Malinovskii, V.K. (1994) Corrected normal approximation for the probability of ruin within finite time, Scandinavian Actuarial Journal, 161–174.Google Scholar
Malinovskii, V.K. (1996a) Limit theorems for stopped random sequences. II: probabilities of large deviations, Theory Probab. Appl., 41, 70–90.Google Scholar
Malinovskii, V.K. (1996b) Approximations and upper bounds on probabilities of large deviations in the problem of ruin within finite time, Scandinavian Actuarial Journal, 124–147.Google Scholar
Malinovskii, V.K. (1998) Non-poissonian claims' arrivals and calculation of the probability of ruin, Insurance: Mathematics and Economics, 22, 123–138.Google Scholar
Malinovskii, V.K. (2000) Probabilities of ruin when the safety loading tends to zero, Advances in Applied Probability, 32, 885–923.Google Scholar
Malinovskii, V.K. (2007) Zone-adaptive control strategy for a multiperiodic model of risk. Annals of Actuarial Science, 2(II), 391–409.Google Scholar
Malinovskii, V.K. (2008a) Adaptive control strategies and dependence of finite time ruin on the premium loading, Insurance: Mathematics and Economics, 42, 81–94.Google Scholar
Malinovskii, V.K. (2008b) Risk theory insight into a zone-adaptive control strategy. Insurance: Mathematics and Economics, 42, 656–667.Google Scholar
Malinovskii, V.K. (2009a) Scenario analysis for a multi-period diffusion model of risk, ASTIN Bulletin, 39, 649–676.Google Scholar
Malinovskii, V.K. (2009b) Survive a downswing phase of the underwriting cycle, 39th ASTIN Colloquium in Helsinki, Finland, 1-4 June 2009.Google Scholar
Owen, G. (1982) Game theory. 2nd Ed., Academic Press.Google Scholar
Pentikäinen, T. (1988) On the solvency of insurers. In: Classical Insurance Solvency Theory, Ed. by: Cummins, J.D. and Derring, R.A., Boston etc., Kluwer, 1988, 1–48.Google Scholar
Rantala, J. (1988) Fluctuations in insurance business results: some control theoretical aspects. In book: Transactions of the 23-rd International Congress of Actuaries, Helsinki 1988, 1, 43–78.Google Scholar
Schlezinger, H. and von der Schulenburg, J.M. (1993) Consumer information and decisions to switch insurers, Journal of Risk and Insurance, LV(4), 591–615.Google Scholar
Soros, G. (1994) The Alchemy of Finance: Reading the Mind of the Market. John Wiley & Sons, Inc. New York, etc. Google Scholar
Subramanian, K. (1998) Bonus-Malus systems in a competitive environment, North American Actuarial Journal, 2, 38–44.Google Scholar
Sun, Ch. (2007) Laplace transform of the survival probability under Sparre Andersen model, Appl. Math. J. Chinese Univ. Ser. B, 22(1), 109–118.Google Scholar
Teugels, J.L. (1982) Estimation of ruin probabilities, Insurance: Mathematics and Economics, 1, 163–175.Google Scholar
Venezian, E.C. (1985) Ratemaking methods and profit cycles in property and liability insurance, Journal of Risk and Insurance, September 1985, 477–500.Google Scholar
von Neumann, J. and Morgenstern, O. (1944) Theory of games and economic behavior. Princeton University Press.Google Scholar
Wang, R. and Liu, H. (2002) On the ruin probability under a class of risk processes, ASTIN Bulletin, 32(1), 81–90.Google Scholar