A Maximum Entropy Approach to Loss Distribution Analysis

In this paper we propose an approach to the estimation and simulation of loss distributions based on Maximum Entropy (ME), a non-parametric technique that maximizes the Shannon entropy of the data under moment constraints. Special cases of the ME density correspond to standard distributions; therefore, this methodology is very general as it nests most classical parametric approaches. Sampling the ME distribution is essential in many contexts, such as loss models constructed via compound distributions. Given the difficulties in carrying out exact simulation, we propose an innovative algorithm, obtained by means of an extension of Adaptive Importance Sampling (AIS), for the approximate simulation of the ME distribution. Several numerical experiments confirm that the AIS-based simulation technique works well, and an application to insurance data gives further insights in the usefulness of the method for modelling, estimating and simulating loss distributions.