SFB 303 Discussion Paper No. B - 82
Author: Sondermann, Dieter
Title: Reinsurance in Arbitrage-Free Markets
Abstract: In this paper we study truly dynamic reinsurance policies which are conditioned on the information
structure, i.e. , which can be revised at any point of time depending on the development of claims, premiums and
interest rates. Under reasonable assumptions it can be shown:
(i) One can restrict oneself to the simplest form of
reinsurance, namely proportional reinsurance contracts. Other forms of reinsurance, like "excess-loss", "stop-
loss", reinsurance with different layers, or, generally, any form of reinsurance which depends on the whole paths
of the claim process (Schadensverlauf) can be valued by reinsurence to the premiums of proportional reinsurance
contracts.
(ii) There is no need to specify preferences over stochastic processes. The valuation method is
preference free.,br>
(iii) Pareto optimal allocations of the total risk may be achieved by proportional (however
dynamic) risk sharing, i.e., through markets. There is no need for complex game theoretical analysis as proposed
by BORCH (1962, 1986 b)The key to this analysis is the "no-arbitrage" condition, i.e., there is no free lunch.
Although a necessary condition for the economy to be in equilibrium it is much weaker than the latter, since it
neither assumes that the markets are perfectly competitive nor that all agents behave rationally. It is sufficient
that a few aware of possible arbitrage opportunities and that their marginal utility of money is positive. The "No-
arbitrage" condition was introduced to financial economics by ROSS (1976 a ). The arbitrage method has been
developed to a powerful tool in option pricing, its analytical method being martingale theory. The present
analysis also makes use of this method.
Keywords:
JEL-Classification-Number:
Creation-Date: March 1988
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