An Extension of Interval Probabilities using Modal Interval Theory and its Application to Non-life Insurance

Abstract In this paper we apply the modal interval theory to the actuarial field to study the analysis and control of solvency in non-life insurance portfolios. The advantages of modal intervals over classical intervals are the interpretative field and the extension of the calculation possibilities that modal intervals offer. To achieve this, we will analyse and propose some properties of modal interval probability that allow us to ensure that the cumulative distribution function and the probability density function of the aggregated cost with which we will work are modal interval functions and, therefore, they can be correctly interpreted from this new point of view.