Global parametric solution

The second section focuses on catastrophe risk models, the technology that makes global risk transfer more seamless and which since the 1980s has had an enormous impact on the industry. The discussion addresses earthquake risk models in particular. These models have played an important role in advances in financial tools that have brought an affluence of capital into earthquake reinsurance. Alternative risk transfer, the convergence market, CAT bonds, parametric solutions, industry indices, and modeled loss triggers, and their importance in earthquake risk transactions are addressed in the third section of the paper. 

Remark 3 Note also that in step 1, step 3a, and step 3b a rather important assumption is made that is, we can find the support functions and for the given values of the multiplier vectors (A,/jl) and (A, p.). The determination of these support functions cannot be achieved in general, since these are parametric functions of y and result from the solution of the inner optimization problems. Their determination in the general case requires a global optimization approach as the one proposed by (Floudas and Visweswaran, 1990 Floudas and Visweswaran, 1993). There exist however, a number of special cases for which the support functions can be obtained explicitly as functions of they variables. We will discuss these special cases in the next section. If however, it is not possible to obtain explicitly expressions of the support functions in terms of they variables, then assumptions need to be introduced for their calculation. These assumptions, as well as the resulting variants of GBD will be discussed in the next section. The point to note here is that the validity of lower bounds with these variants of GBD will be limited by the imposed assumptions. 

The steady-state equations describing lumped parameter systems in which several reactions occur simultaneously contain a very large number of parameters. Thus, it is impractical to conduct an exhaustive parametric study to determine their features. The new technique presented here predicts qualitative features of these systems such as the maximum number of solutions, parameter values for which these solutions exist and all the local bifurcation diagrams. Construction of the three varieties enables the division of the global parameter space into regions with different bifurcation diagrams. 

---