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Dynamic Equilibrium and the Structure of Premiums in a Reinsurance Market

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  • Knut K. Aase

    (Norwegian School of Economics and Business Administration, 5035 Bergen, Norway)

Abstract

In this paper we present an economic equilibrium analysis of a reinsurance market. The continuous-time model contains the principal components of uncertainty; about the time instants at which accidents take place, and about claim sizes given that accidents have occurred.We give sufficient conditions on preferences for a general equilibrium to exist, with a Pareto optimal allocation, and derive the premium functional via a representative agent pricing theory. The marginal utility process of the reinsurance market is represented by the density process for random measures, which opens up for numerous applications to premium calculations, some of which are presented in the last section.The Hamilton-Jacobi-Bellman equations of individual dynamic optimization are established for proportional treaties, and the term structure of interest rates is found in this reinsurance syndicate. The paper attempts to reach a synthesis between the classical actuarial risk theory of insurance, in which virtually no economic reasoning takes place but where the net reserve is represented by a stochastic process, and the theory of equilibrium price formation at the heart of the economics of uncertainty. The Geneva Papers on Risk and Insurance Theory (1992) 17, 93–136. doi:10.1007/BF00962709

Suggested Citation

  • Knut K. Aase, 1992. "Dynamic Equilibrium and the Structure of Premiums in a Reinsurance Market," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 17(2), pages 93-136, December.
    • Handle: RePEc:pal:genrir:v:17:y:1992:i:2:p:93-136
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    Cited by:

    1. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    2. Knut K. Aase, 2022. "Optimal Risk Sharing in Society," Mathematics, MDPI, vol. 10(1), pages 1-31, January.
    3. Aase, Knut K., 2006. "Optimal Risk-Sharing and Deductables in Insurance," Discussion Papers 2006/24, Norwegian School of Economics, Department of Business and Management Science.
    4. repec:dau:papers:123456789/5590 is not listed on IDEAS
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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