Optimal Multistage Portfolio Management Using a Parallel

We present a multi-stage model for allocation of financial resources to different currencies. The model is tested using a three-stage scenario tree with a mean-reversion property. For solving three-stage stochastic programs the interior point method (IPM) in the frame of the primal-dual path-following formulation is used. Because the matrix of the corresponding linear system is large, sparse and regular, it can be easily stored in a compressed format. The compressed storage is further used in calculating the right-hand side of the linear system and the objective function. An application of the BQ method to the IPM allows decomposition of the large linear system to smaller blocks allowing thus solving it in parallel. The parallel code is designed for clusters of SMP's and written in the Fortran/MPI language. The linear algebra operations on the small block matrices are executed by the LAPACK library calls. The achieved results have proved that by increasing the number of stages the quality of the optimal decision could be improved. 1. Introduction. Recently an interest in the development of multistage models of portfolio management could be observed. At this place we refer to successful and valuable contributions of [1], [2] and [3]. In [4] a multi-period dynamic model for fixed-income portfolio management under uncertainty, using multi-stage stochastic programming was developed. The scenarios of the term structure of interest rates were generated using Monte Carlo simulations. Their results confirmed that multi-period models outperform classical single-period models. We present an example of a portfolio management problem. It is a model for allocation of financial resources to bond indices in different currencies. The stochastic properties are represented in the form of a scenario tree. The scenarios contain future possible developments of interest rates and exchange rates. When one deals with several currencies, the realistic scenario trees are " bushy " and the number of scenarios grows exponentially with the number of stages. Thus, the computation of such problems could be extremely large and computationally intractable. Approaches for solving these problems usually either take advantage the problems' matrix structure or decompose the problem into smaller subproblems. In the literature we can also see a considerable research effort to develop efficient parallel methods for solving this problem on parallel computer architectures. In our paper we demonstrate a parallel interior point algorithm (IPM) for solving three-stage stochastic linear problem which comes from a three-period models of portfolio management. The paper is organized …