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Optimal Asset Allocation for Defined Contribution Pension Schemes

By D.T. Koops


In recent years there has been a growing demand for defined contribution (DC) pension schemes in the Netherlands. We consider individual DC schemes, in which the objective is to invest the contributions of the participants in such a way that they receive an `optimal' pension. To mathematically describe what an optimal pension is, we make use of utility functions. The utility function incorporates the willingness of the participant to take risks in order to get a higher expected return. Since the problem is essentially a dynamic portfolio problem, we first consider the mathematical literature about solution methods in portfolio theory. One of the two main analytical methods relies on dynamic programming in continuous time, which results in a partial differential equation. The other method we consider is based on martingale theory. An important property of defined contribution pension schemes, is that contributions are deposited regularly. We incorporate this into the problem and we consider some cases in which an analytical solution can be derived, using both theoretical methods that we studied. In the existing literature, there are no known analytical methods when the labour income is stochastic and not perfectly correlated with the market. We consider several numerical approaches for this problem. We find that discrete-time dynamic programming leads to the most flexibility. Therefore, to tackle this case, we develop and implement an algorithm that relies on (discrete-time) dynamic programming. We test and verify the results of the algorithm in cases that an analytical solution is available

Topics: Portfolio theory, dynamic programming, martingale method, defined contribution, pension, numerical method
Year: 2014
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