A Lognormal Model for Insurance Claims Data

Abstract

In the insurance area, especially based on observations of the number of claims, N(w), corresponding to an exposure w, and on observations of the total amount of claims incurred, Y (w), the risk theory arises to quantify risks and to fit models of pricing and insurance company ruin. However, the main problem is the complexity to obtain the distribution function of Y (w) and, consequently, the likelihood function used to calculate the estimation of the parameters.

This work considers the Poisson(wλ), λ>0, for N(w) and lognormal(µ, σ² ), −∞<µ 0, for Z_i , the individual claims, and presents maximum-likelihood estimates for λ, µ and σ² .