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...technical financial stability insurance companies. The purpose of this paper is to calculate the reserve in a decision-making environment, so that estimates can be made according to accurately defined and previously established rational criteria. Specifically, the estimating process enables a company's particular situation to be taken into account, by incorporating its approach to the consequences arising from estimation errors into the model. The proposed calculation method gives rise to optimum link ratio estimators that can also be interpreted from a Bayesian perspective, with the advantages associated to such methodology. (JEL G22)
Introduction
Determining of the outstanding claims amount and appropriate calculating of reserves allocated to such is an essential part of general insurance company activities. In particular, among insurance companies, link ratio based methods stand out substantially.
The first attempt to stochastically generalize this type of method was with the de Vylder [1978] least squared model, the starting point for the work done by Mack [1994] in which the estimation of link ratios is carried out by using a linear regression model, the original stochastic model later being updated and modified. This is the case of the work by Halliwell [1996] that performs estimates of stochastic model parameters with the generalized least squares technique, and that of the Australians, Barnett and Zehnwirth [1998] with their "extended link ratio family." A different line of thought was that of Kremer [1982] who provided the basis for the Verrall [1994] two-way factor variance analysis model, which was also later subject to certain improvements using Bayesian methods, state-space models, and generalised linear or additive models, by England and Verrall [1999].
Essentially, these stochastic generalisations are linear models with different variables that are dealt with differently. In this context, it is possible to approach the problem from a new perspective by calculating an Outstanding Claims Reserve using the above-mentioned link ratios. The decision framework from which the issue is approached enables decision makers to intervene in such structure, mainly materialised in the minimax hypothesis, which reflects a sensible attitude on their part, moderated by the restrictions imposed on the range of claims accumulated over development periods. The consequences of choices made are expressed by a loss function construed as the arithmetic sum of squared estimation...
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