A survey of scenario generation methods for asset-liability management

Asset-liability management (ALM) attempts to find the optimal investment strategy under uncertainty in both the asset and liability streams. The ALM problem can be of interest to both private investors and banks or insurance companies. In fact, while a private investor may need to consider also the liabilities, as he may wish to plan his personal investments accounting for future consumption decisions that he has already planned; on the other hand an insurance company or a bank must take liabilities into consideration as they have payments to customers and employees that must be satisfied. In order to obtain reliable results in this portfolio optimization problem, it's important to focus on the scenario generation. A good scenario generation method allows the investor, not only to trust the output, but also to have a saving in terms of calculation power. In the present work we study the impact of different scenario generation methods on the results of ALM problem in stochastic programming. Firstly we investigate the best ALM problem formulation for the survey by studying the results of a more basic formulation, with different assumptions on the asset returns distribution and only one deterministic liability, and a more complete formulation in which we add the transaction costs, we consider the asset prices, random liabilities and more decision variables. Finally we focus on the comparison between the results obtained with different scenario tree structures and different scenario generation methods: Monte Carlo, Antithetic Sampling, Control Variates and Quasi Monte Carlo with low discrepancy sequences. The comparison is made, besides looking at the quality and stability of the solution, also solving the problem for many periods in order to choose as better scenario generation method the one that allows the investor to cover a very long time period with his current investment strategy decision.