J. Gondzio and A. Grothey
Abstract
Stochastic programming is recognized as a powerful tool to help
decision making under uncertainty in financial planning.
The deterministic equivalent formulations of these stochastic
programs have huge dimensions even for moderate numbers of assets,
time stages and scenarios per time stage. So far models treated
by mathematical programming approaches have been limited to simple
linear or quadratic models due to the inability of currently
available solvers to solve NLP problems of typical sizes.
However stochastic programming problems are highly structured.
The key to the efficient solution of such problems is therefore
the ability to exploit their structure.
Interior point methods are well-suited to the solution of very
large nonlinear optimization problems. In this paper we exploit
this feature and show how portfolio optimization problems with
sizes measured in millions of constraints and decision variables,
featuring constraints on semi-variance, skewness or nonlinear
utility functions in the objective, can be solved with the
state-of-the-art solver.
Key words: Nonlinear Programming, Portfolio Optimization, Interior Point Methods, Parallel Computing.