ON INTEGRATED CATASTROPHIC RISK MANAGEMENT

摘要

The model outlined in Section 4 can be used for risk management with the so-called rolling horizon. The model includes a time horizon τ , which may be a random variable, say the time of the first catastrophe from the given initial state at t = 0. This generates a sequence of decisions for t = 0,1,... . After implementing decisions at t = 0, new information becomes available. At t = 1 the model is updated, a new sequence of decisions for t = 1,2,... with a new time horizon is obtained, decisions for t = 1 are implemented, and so on. Thus, in risk management with a rolling time horizon expectations within a time horizon τ are used to find and implement decisions at each current step t = 0,1,... . Several data-intensive numerical experiments with the type of models outlined in this paper are discussed in [1], [5-6]. In these experiments data on earthquakes from Russia and Italy are used. The generator of earthquakes is designed in a way suitable for on-line adaptive Monte Carlo optimization. It uses regional maps of seismic activities, macroseismic intensities, and the geo-tectonic structure. On the basis of these maps the over-time occurrence of earthquakes is generated at different locations. The time horizon in these experiments coincides with time τ of the first catastrophe. Given the distributions of the return time for each seismic zone i, the time of the next earthquake θ_ i, in each i can be sampled. Then τ is calculated as τ = min_i θ_i. All values at risk in the region are subdivided into several categories according to their vulnerability. Given a macroseismic intensity and a probability distribution of damage for a given category of buildings, losses L_j~t are simulated for each location j. The model has been implemented in Matlab on a Pentium 450MHz. The solution time of a problem with 300 decision variables, 200 locations, and up to 2000 fast Monte Carlo catastrophe simulations was about 20-40 minutes. In some cases the model can be reduced to a linear programming model, but it will require at least 2000x300 additional variables. The purpose of the experiments in the region Irkutsk, Russia, was to analyze the feasibility of catastrophe coverage for insurance companies under different attitudes to risks and different initial risk reserves. In the region the emergency of a viable insurance industry is slow and subject to insolvency risks. In our ex- periments we used different numbers of imaginative companies. We observed considerable improvements with respect to overpayments of individuals and their profits through the ability of the model to deal with the contribution of individual risks to these indicators. In particular, the important characteristic of the optimal solutions is the sharing of the same risks by different companies. The model tends to select "almost" mutually independent or/and compensating each other (i.e., negatively correlated) fractions of different risks. A flood management model for a European region is created at IIASA. This model will incorporate in the same integrated manner the geo-physical characteristics of the region, hydraulic and hydrological equations of floods, the vulnerability of buildings and the agricultural yields, socio-economic data and various feasible policy options.