Numerical algorithms for Panjer recursion by applying Bernstein approximation

In actuarial science, Panjer recursion (1981) is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculation for the compound distribution by applying Panjer recursion will involve an approximation of the integration. In order to simplify the numerical algorithms, we apply Bernstein approximation for the continuous severity distribution function and obtain approximated recursive equations, which are used for computing the approximated values of the compound distribution. The theoretical error bound for the approximation is also obtained. Numerical results show that our algorithm provides reliable results.