We use the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for catastrophic 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...

We examine the Laplace transform of the distribution of the shot noise process using the martingale. Applying the piecewise deterministic Markov processes theory and using the relationship between the shot noise process and the accumulated/discounted aggregate claims process, the Laplace...

The new Solvency II regime and the upcoming IFRS 4 Phase II regime bring significant changes to current reporting of insurance entities, and particularly in relation to valuation of insurance liabilities. Insurers will be required to valuate their insurance liabilities on a risk-adjusted basis...

Under the Solvency II Directive insurers are required to allow for all possible events when setting their technical provisions, including those that may not have been historically realised before. Such events not presented in a set of observable historical loss data are often called Binary...