Bayesian estimation of structure variables in the Collective Risk Model for reserve risk

Reserve risk represents a fundamental component of underwriting risk for non-life insurers and its evaluation can be achieved through a wide range of stochastic approaches, including the Collective Risk Model. This paper, in order to fill a gap in existing literature, proposes a Bayesian technique aimed at evaluating the standard deviation of structure variables embedded into the Collective Risk Model. We adopt uninformative prior distributions and the observations of the statistical model are obtained making use of Mack’s formula linked to bootstrap methodology. Moreover, correlation between structure variables is investigated with a Bayesian method, where a dependent bootstrap approach is adopted. Finally, a case study is carried out: the Collective Risk Model is used to evaluate the claims reserve of two non-life insurers characterized by a different reserve size. The claims reserve distribution is examined with respect to the total run-off and the one-year time horizon, enabling the assessment of the reserve risk capital requirement.