Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 43 / 4 / a / Solution

With fixed positive prior parameters and $m_i\ge 1$, total exposure satisfies $M={\sum }_{i=1}^k{m}_i\ge k$. Hence $M\to \infty$ as the number of observed years grows, andThus the credibility estimate places asymptotically all its weight on the observed policy-weighted claim frequency. The assertion concerns the credibility weight; the scale of the predicted number of claims still includes the known next-year exposure $m_{k+1}$.