Discretized reality and spurious profits in stochastic programming models for asset/liability management

In the literature on stochastic programming models for practical portfolio investment problems, relatively little attention has been devoted to the question how the necessarily approximate description of the asset-price uncertainty in these models influences the optimal solution. In this paper we will show that it is important that asset prices in such a description are arbitrage-free. Descriptions which have been suggested in the literature are often inconsistent with observed market prices and/or use sampling to obtain a set of scenarios about the future. We will show that this effectively introduces arbitrage opportunities in the optimization model. For an investor who cannot exploit arbitrage opportunities directly because of market imperfections and trading restrictions, we will illustrate that the presence of such arbitrage opportunities may cause substantial biases in the optimal investment strategy.