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QuasiNewton methods for OrderValue Optimization and ValueatRisk calculations
 

Summary: Quasi­Newton methods for Order­Value
Optimization and Value­at­Risk calculations
R. Andreani # J. M. Mart’nez + M. Salvatierra # F. Yano §
October 25, 2004, 17.45 hs.
Abstract
The OVO (Order­Value Optimization) problem consists in the min­
imization of the order­value function F p (x), defined by
F p (x) = f i p (x) (x),
where
f i 1 (x) (x) # . . . # f i m (x) (x).
The functions f 1 , . . . , f m are defined on # # IR n and p is an integer
between 1 and m.
When x is a vector of portfolio positions and f i (x) is the predicted
loss under the scenario i, the order­value function is the discrete Value­
at­Risk (VaR) function, which is largely used in risk evaluations.
The OVO problem is continuous but nonsmooth. A Cauchy­like
method with guaranteed convergence to points that satisfy a first or­
der optimality condition was recently introduced by Andreani, Dunder
# Department of Applied Mathematics, IMECC­UNICAMP, University of Campinas,
CP 6065, 13081­970 Campinas SP, Brazil. This author was supported by PRONEX­

  

Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas

 

Collections: Mathematics