High Performance Computing for Asset Liability Management

Jacek Gondzio and Roy Kouwenberg

Financial institutions require sophisticated tools for risk management. For company-wide risk management both sides of the balance sheet should be considered, resulting in an integrated asset liability management approach. Stochastic programming models suit well these needs and have already been applied in the field of asset liability management to improve financial operations and risk management. The need of dealing with a long term planning horizon inevitably leads to multiple decision stages (trading dates) in the stochastic program and results in an explosion of dimensionality. In this paper we show that dedicated model generation, specialized solution techniques based on decomposition and high performance computing are the essential elements to tackle these large scale financial planning problems. It turns out that memory management is a major bottleneck when solving very large problems, given an efficient solution approach and a parallel computing facility. In this paper we report on the solution of an asset liability management model for an actual Dutch pension fund which includes contribution policies and takes into account transaction costs. The model allows for 6 portfolio rebalancing dates and up to 13 realizations to approximate the conditional return distributions. This leads to a model with 4,826,809 scenarios, 12,469,250 constraints and 24,938,502 variables, which is the largest stochastic linear program ever solved.

Technical Report MS-99-004, Department of Mathematics and Statistics, The University of Edinburgh, Scotland. May 21, 1999.

Contact: gondzio@maths.ed.ac.uk