Solving ALM problems via sequential stochastic programming

Abstract

In this paper, an approximation of dynamic programming using sequential stochastic programming is introduced to solve long-term dynamic financial planning problems. We prove that by approximating the true asset return dynamics by a set of scenarios and re-solving the problem at every time-step, we can solve in principle the dynamic programming problem with an arbitrarily small error. The dynamic programming algorithm is effected on the approximate sample return dynamics by means of stochastic programming. This method is applied to the problem of a fund that guarantees a minimal return on investments. This minimal return guarantee is the liability of the fund. The dynamic portfolio management problem consists of maximizing the multi-period return while limiting the shortfall with regard to the guaranteed return. The problem is tested in an 8 year out-of-sample backtest from the perspective of a Swiss fund that invests domestically and in the EU markets and faces transaction costs.

Keywords:

• Asset and liability management
• Stochastic programming
• Dynamic programming
• Multi-period portfolio optimization

Acknowledgements

The authors wish to acknowledge the comments of three anonymous referees and thank the Editor-in-Chief for his detailed comments and corrections which materially improved the paper.