Application of multistage stochastic programs solved in parallel in portfolio management

Authors:
Maria Lucka;Igor Melichercik;Ladislav Halada
Affiliations:
Faculty of Education, University of Trnava, Priemyselna 4, 918 43 Trnava, Slovakia and Institute of Scientific Computing, University of Vienna, Nordbergstrasse 15/C/3, A-1090 Vienna, Austria;Department of Applied Mathematics and Statistics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, 842 48 Bratislava, Slovakia;Institute for Informatics, Slovak Academy of Sciences, Dubravska 9, 842 37 Bratislava, Slovakia
Venue:
Parallel Computing
Year:
2008

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Abstract

We present a multistage model for allocation of financial resources to bond indices in different currencies. The model was tested on historical data of interest and exchange rates. We compare a two-stage and a three-stage stochastic programming model from a financial performance point of view. For solving two-stage and three-stage stochastic programs the interior point method (IPM) in the frame of the primal-dual path following formulation is used. An application of the Birge and Qi factorization to the IPM allows decomposition of large linear system to smaller blocks allowing thus to solve it in parallel. The parallel code is written in the Fortran programming language, using the message passing interface (MPI) for communication. Parallel and financial performance is illustrated on experiments executed on the IBM 1350 Linux cluster.