Abstract
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.