A Lognormal Model for Insurance Claims Data

• 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, σ), −∞<μ<∞, and σ > 0, for Zi, the individual claims, and presents maximumlikelihood estimates for λ, μ and σ. Key-Words: • lognormal distribution; maximum-likelihood estimation; number of claims; total amount of claims. AMS Subject Classification: • 62J02, 62F03. 132 Zuanetti, Diniz and Leite A Lognormal Model for Insurance Claims Data 133