Best estimate of the motor liability claims reserve under the direct reimbursement scheme

In some European countries, a large subset of motor liability claims is managed under a direct reimbursement (DR) scheme. The first component that loss adjustors use to evaluate the claims reserve is given by the sum of the estimated provision for each outstanding claim (known as case reserves). Due to the heterogeneity of data available, the introduction of direct indemnity in third-party liability insurance has resulted in greater attention to the traditional statistical-actuarial methods used to control and/or verify the evaluations. This paper presents the first results of a study undertaken to define a new calculation method that enables quantifying the claims reserve using different hypotheses of the evolution of settlement mechanisms and in so doing offers greater transparency, objectivity as well as the opportunity to perform stress tests. A numerical application is presented comparing the results of the proposed model with those using traditional statistical methods.