Study Of Dependence Models Of Claim Run-off Triangles In Claim Reserving

In recent years, studying dependence structure between claim payments has be-come one of the most significant issues in claim reserving. Most classical models of run-off triangles cannot deal with this issue, whereas other dependence models have strong limitations. In this paper, we first give a log normal variance mixture model which can cope with any correlation structures between claim development factors. We also derive closed-form expressions for estimation of claim reserves and its mean squared error prediction. Then we further generalizes the first model to a log normal variance mixture copula model, in which the correlation structure is preserved and more types of risks can be handled. We present the method of Monte Carlo simulation to cal-culate not only estimation of claim reserves and its mean squared error prediction but also other results like VaR about claim reserves. Finally, we discuss issues concerning model and parameter selection in applications illustrated through a numerical example.