A Multiple Constrains Risk Optimization Model Solution Of Alpha-superquantile Based On The Worst Case And Its Application

Risk management is not only the important topic in the finance research, but alsoit has been widely studied and applied in structural reliability system. The mainpurpose is to look for the optimal structure design, which satisfies the reliabilityconstraint that is less than a given threshold value. In this paper, we set up the riskoptimizationWCVaR model under the uncertainty distribution, moreover, the model andalgorithm are successfully applied to the reliability system considering the relatedoptimal structure design issues. The whole paper is divided four chapters.In the first section, we mainly introduce the research background, significance,research status at home and abroad and the innovation in this paper, meanwhile, wealso interpret the Lagrange duality theory and the smoothing method theory.In the second section, we introduce the relevant theory of alpha-superquantileand WCVaR , then we discuss some key theory and uncertainty distributions. Moreover,we analysizeWCVaR model under the discrete box distribution.In the third section, we use relevant probability theory to present some detailedexplore and arguments about the buffered failure probability framework, such someequivalence proofs and so on.In the fourth section, under the box discrete distribution of random variables, weset up the risk optimizationWCVaR model and consider several limit-state functions.However, this model is composed of min-max-type optimization problem. With thelinear objective function, we reduce the formulation to linear programming problem.The relationship of the solutions between the proposed model and the reduced one isproved equivalently, moreover, we solve the model by linear method and smoothingmethod in the system reliability.