Solving ALM problems via sequential stochastic programming

• Published in: Quantitative finance Vol. 7; no. 2; pp. 231 - 244
• Main Authors: Herzog, Florian, Dondi, Gabriel, Keel, Simon, Schumani, Lorenz M., Geering, Hans P.
• Format: Journal Article
• Language: English
• Published: Bristol Routledge 01.04.2007; Taylor and Francis Journals; Taylor & Francis Ltd
• Series: Quantitative Finance
• Subjects: Approximation; Asset and liability management; Asset liability management; Dynamic programming; Multi-period portfolio optimization; Optimization algorithms; Portfolio management; Problem solving; Stochastic models; Stochastic programming; Studies; Switzerland; Europe
• ISSN: 1469-7688; 1469-7696
• DOI: 10.1080/14697680701272575

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.