 
Summary: Global OrderValue Optimization by means of a
multistart harmonic oscillator tunneling strategy
R. Andreani # J. M. Mart’nez + M. Salvatierra # F. Yano §
July 15, 2004
Abstract
The OVO (OrderValue Optimization) problem consists in the min
imization of the ordervalue function f(x), defined by
f(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 and, usually, has
many local minimizers. A local method with guaranteed convergence
# Department of Applied Mathematics, IMECCUNICAMP, University of Campinas,
CP 6065, 13081970 Campinas SP, Brazil. This author was supported by PRONEX
