Stochastic modelling of insurance liabilities
Keywords:claim prize, dependence characteristics, development time, multivariate copulas, loss adjusted expense, IBNR reserve
Our aim is to present a method for estimating incurred but not reported (IBNR) claim reserves. Each claim is described by three
characteristics: 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.