The focuses are on the study of risk management of natural disasters from the perspective of complex systems, using the example of Mexico. It develops the theory of an arrival process taking into account an early warning system and we use it to create appropriate actuarial models. Then, it formulates 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 with the use of the Föllmer-Schweizer strategy.