Management of catastrophic risks considering the existence of early warning systems

It is crucially important to incorporate the notion of early warning systems in insurance mathematics. We develop the theory of an arrival process taking into account an early warning system, and we use it to create appropriate actuarial models. Then, we formulate a stochastic optimization problem to find an investment strategy for the management of a fund from the perspective of a risk-averse government. The solution is given using the Föllmer-Schweizer strategy.