High performance computing and economic scenario generation: Integrating expert forecasts into plane price modeling

Abstract

The problem at hand is the integration of expert forecasts for plane prices into a fully calibrated basic economy. The economy is simulated through an Economic Scenario Generator (ESG), which includes macroeconomic processes, interest rate term structures, etc.. By defining the available best-case, worst-case, and mid-case forecasts to correspond to the 95%, the 50% and the 5% quantiles of the plane price distribution, one could describe the problem with the following optimization setting: min(βc,α c,i,δ′c, ,σc,i){|| (Q (ĨT,S) ⊙ P̃Rc,i,T,S(βc, αc,i, δ′c, γ′c, σc,i), q)-FM̃) ⊙ W||2F} The tilded matrices represent simulation results, i.e. they have the dimension timesteps T and scenarios S. The function Q(M̃T,S, q) : ℝT.S × [0, 1]q → ℝT.q is mapping a matrix M̃ T,S, q of simulated scenarios with dimension (T×S) onto each timestep's quantiles q , resulting in a matrix of dimension T×q. FM is the (T×q) matrix of expert forecasts, and W is a (T×q) weighting matrix. |||| F denotes the Frobenius norm, and ⊙ is the element-wise multiplication. The economy simulation is computation-intensive, for which we take benefit of using GPGPU techniques. The optimisation part is also a high-dimensional computation-intensive problem, for which we use a natural computing approach using Differential Evolution. © 2011 Springer-Verlag Berlin Heidelberg.