Reserving using the Gaussian approximation to the Cox process with shot noise intensity

We employ the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for common events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic Markov processes theory. Since the claim intensity is not observable we employ state estimation on the basis of the number of claims i.e. we obtain the Kalman-Bucy filter. In order to use the Kalman-Bucy filter, the claim arrival process (i.e. the Cox process) and the claim intensity (i.e. the shot noise process) should be transformed and approximated to two-dimensional Gaussian process. Based on this filter, we derive reserving formulae at any time for common events with and without stop-loss reinsurance contract. We also examine the effect on reserves caused by change in the values of the security loading and the retention limit.

Paper Presentation

Keywords: The Cox process; Shot noise process; Piecewise deterministic Markov processes theory; The Kalman-Bucy filter; Reserving.