臺灣博碩士論文加值系統

在論文中首先介紹由金融分析中產生的CVaR和VaR的最小化問題。在考慮問題為一個線性方程之下，我們試著去找VaR的最小解。我們發展出一個新方法求得絕對最佳化解並解釋其中原理。而在最後則提出問題加以舉例。

In this paper,first we introduce the convex minimization problem of the
conditional value-at-risk(CVaR) and value-at-risk(VaR) that arises from-
nancial risk analysis. By considering these problems as linear programs, we
want to find the minimum of VaR. We develop a global method to minimize
the VaR and show the procedure will attain to a global optimal. Moreover,
a numerical example is provided to illustrate the methodology.

Contents
1Introduction........................2
2TheCVaRandVaRMinimizationProblems........................4
2.1DescriptionofTheApproach...................4
2.2TheCVaRMinimizationProblem................6
2.3AnLPECFormulation......................7
3AGlobalMethodtoMinimizetheValue-at-Risk11
3.1Descentdirection.........................11
3.2DescentAlgorithm........................15
4NumericalExperiments........................17
5Conclusions........................21
6References........................22

References
[1]Jong-Shi Pang and SvenLeyer.On the Global Minimization of the
value-at-risk. Mathematics and Computer Science Division, Argonne
National Laboratory Preprint ANL/MCS-P1112-1203(2004).
[2]R.T.Rockafellar and S.Uryasev. Optimization of conditional value-
at-risk. Journal of Risk2(2000)21-41.
[3]R.T.Rockafellar and S.Uryasev.Conditional value-at-risk for general
loss distribution. Journal of Banking and Finance 26(2002)1443-
1471.
[4]O.L.Mangasarian. Regularized linear programs with equilibrium
constraints. In M.Fukushima and L.Qi, editors. Reformulation-
Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Meth-
ods. Kluwer Academic Publishers(Dordercht1998)pp.259-268.
[5]R.T. Rockafellar. Convex Analysis. Princeton Mathematics,Vol.28,
Princeton Univ.Press(1970).
[6]N.Z.Shor. Minimization Methods for Non-Dierentiable Functions.
Springer-Verlag(1985).
[7]A.Shapiro and Y.Wardi.Non-dierentiability of the Steady-State
Function in Discrete Event Dynamic System.IEEET ransactionson
Automatic Control,Vol.39,(1994)1707-1711.