Summary: Quasi�Newton methods for Order�Value
Optimization and Value�at�Risk calculations
R. Andreani # J. M. Mart��nez + M. Salvatierra # F. Yano �
October 25, 2004, 17.45 hs.
Abstract
The OVO (Order�Value Optimization) problem consists in the min�
imization of the order�value 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 order�value function is the discrete Value�
at�Risk (VaR) function, which is largely used in risk evaluations.
The OVO problem is continuous but nonsmooth. A Cauchy�like
method with guaranteed convergence to points that satisfy a first or�
der optimality condition was recently introduced by Andreani, Dunder
# Department of Applied Mathematics, IMECC�UNICAMP, University of Campinas,
CP 6065, 13081�970 Campinas SP, Brazil. This author was supported by PRONEX�

Source: Andreani, Roberto - Instituto de Matem�tica, Estat�stica e Computa��o Cient�fica, Universidade Estadual de Campinas

Collections: Mathematics