Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory

A Smoothing Method for Solving Model under WCVarR

Author HuQinQin
Tutor TongXiaoJiao
School Changsha University of Science and Technology
Course Computational Mathematics
Keywords conditional value-at-risk(CVaR) worst-case conditional value-at-risk (WCVaR) box discrete distribution smoothing method
CLC O224
Type Master's thesis
Year 2011
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The smoothing method is an imporant method for solving nonsmooth problems and has its advantage. For example, the smoothing method can use ordinary derivative conveniently and can retain nice convergence properties, the basic idea of the smoothing method is to approximate a nonsmooth function by the sequence of smoothing functionsBased on the concept of the worst-case conditional value-at-risk,this paper focuses on the computation issue of the profit-risk robust portfolio models.Such model has min-max construction. We transfrom the models into linear programming problems by duality theory. The smooth method is introduced to solving the models. Under the box discrete distribution of random variables, this paper presents the smoothing method of portfolio models and a smoothing algorithm. Furthermore, the global convergence is investigated. These also are innovations. The primary contents are as follows:In the first section, we mainly introduce research backgrond, meaning,research actuality the major work, the arrangement of structure and sign instructions.In the second section, we mainly introduce the definition of semismooth and smoothing methods. We discuss some very important theory about distribution uncertainty(such as mixture distribution uncertainty and discrete distribution). We intrduce the definition of WCVaR, smoothing function of maximal function, properties and smoothing function in WCVaR formula.In the third section, under the box discrete distribution of random variables, this paper presents the smoothing method of three profit-risk robust portfolio models and a smoothing algorithm.Furthermore,the global convergence is investigated. numerical simulations are maken. The results show that the theoretical analysis is correct and the new models are valid.

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