Summary: QuasiNewton methods for OrderValue
Optimization and ValueatRisk calculations
R. Andreani # J. M. Martnez + M. Salvatierra # F. Yano §
October 25, 2004, 17.45 hs.
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),
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