A Stochastic Minimax Model to Calculate Outstanding Claims

Abstract

Correct estimation of the Outstanding Claims Reserve, an item that includes Incurred But Not Reported Claims (IBNR) as well as Incurred But Not Enough Reserved Claims (IBNER), is one of the most important issues currently facing actuarial science, due to its effect on the technical and financial stability of 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.