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Financial institutions require sophisticated tools for risk management. For companywide risk management, both sides of the balance sheet should be considered, resulting in an integrated asset-liability management approach. Stochastic programming models suit these needs well and have already been applied in the field of asset-liability management to improve financial operations and risk management. The dynamic aspect of the financial planning problems 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. We report on the solution of an asset-liability management model for an actual Dutch pension fund with 4,826,809 scenarios; 12,469,250 constraints; and 24,938,502 variables; which is the largest stochastic linear program ever solved. A closer look at the optimal decisions reveals that the initial asset mix is more stable for larger models, demonstrating the potential benefits of the high-performance computing approach for ALM.
1. INTRODUCTION
We are concerned in this paper with the real-life financial planning problem of a Dutch pension fund. The majority of Dutch pension funds use operations research techniques to plan their investment decisions, funding decisions, and risk management. Most Dutch pension funds rely on the commercial hybrid simulation and optimization system described by Boender (1997). The system of Boender considers only static investment strategies or dynamic strategies based on a given decision rule. One way of modeling the dynamic features of the underlying decision problem is to apply the stochastic programming approach. This approach seems to be widely accepted for solving dynamic asset-liability management problems (Bradley and Crane 1972, Kusy and Ziemba 1986, Carino et al. 1994, Mulvey and Vladimirou 1992, Zenios 1995, Consigli and Dempster 1998).
Unfortunately, there are two factors that cause an explosion of dimensionality in the stochastic programming approach applied to asset-liability management. The size of the problem grows exponentially with the number of portfolio rebalancing dates. Moreover, to be sufficiently precise, a discrete approximation of the conditional distribution of the...