Open AccessStochastic modelling of insurance liabilities
Author(s) -
Gaida Pettere
Publication year - 2009
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2009.13.03
Subject(s) - econometrics , marginal distribution , joint probability distribution , univariate , pareto principle , generalized pareto distribution , log normal distribution , multivariate statistics , lomax distribution , statistics , economics , actuarial science , mathematics , random variable , extreme value theory
Our aim is to present a method for estimating incurred but not reported (IBNR) claim reserves. Each claim is described by threecharacteristics: the claim size, the allocated loss adjusted expense and the development time. We concentrate on the joint study of all three random variables. First, the marginal univariate distributions are estimated using families of lognormal, Pareto, Wald and Gamma distributions. Next, the matrix of dependence characteristics is found between the three variables and then different multivariate copulas are used to model the joint distribution. The obtained models are fitted to the real data of motor liability insurance of a Latvian insurance company. By simulation the average claim size and allocated loss adjustment expenses in each development day have been estimated. Finally, outstanding claim reserve has been estimated.