A stochastic model to evaluate pricing distortions in indemnity insurance methods for MTPL insurance

Direct compensation or the direct reimbursement scheme is an indemnity insurance method that many European and American countries use to manage motor liability claims in which the driver that suffers an accident is paid by his/her insurance company that possibly later receives a flat-rate reimbursement (known as forfeit). Using non-life actuarial methodologies, this article analyses the distortion effects due to the direct compensation mechanisms and the effects of different forfeit reimbursement systems on policyholder tariffs in the management of motor liability claims involving vehicles in two different sectors, i.e. automobile and motorcycle. We empirically analyse and formalize the distortion effects resulting from the mechanism that different direct reimbursement systems produce, and explore the correlation between increasing tariffs for motorcycle policyholders and decreasing tariffs for other vehicle policyholders. We propose some alternative methods to overcome these distortion effects, evaluating their pricing impact through a stochastic model applied to a case study.