Forecasting the maximum compensation offer in the automobile BI claims negotiation process

Most motor bodily injury (BI) claims are settled by negotiation, with fewer than 5% of cases going to court. A well-defined negotiation strategy is thus very useful for insurance companies. In this paper we assume that the monetary compensation awarded in court is the upper amount to be offered by the insurer in the negotiation process. Using a real database, a log-linear model is implemented to estimate the maximal offer. Non-spherical disturbances are detected. Correlation occurs when various claims are settled in the same judicial verdict. Group wise heteroscedasticity is due to the influence of the forensic valuation on the final compensation amount. An alternative approximation based on generalized inference theory is applied to estimate confidence intervals on variance components, since classical interval estimates may be unreliable for datasets with unbalanced structures.