Financial asset-pricing theory and stochastic programming models for asset/liability management: A synthesis

Practical portfolio investment problems under uncertainty can be modeled well as multi-period stochastic programs. However, the numerical optimization methods that need to be used to solve such models seriously limit the level of detail in the uncertainty about future asset prices and returns that can be incorporated. Somewhat surprisingly, the question how this necessarily approximate description of the uncertainty should be constructed has received relatively little attention in the stochastic programming literature. Moreover, many of the descriptions that have been used are not arbitrage-free, and therefore inconsistent with modern financial asset-pricing theory. In this paper we will present aggregation methods that can be used in combination with financial asset-pricing models to obtain a description of the uncertainty that is arbitrage-free, consistent with observed market prices as well as concise enough for a stochastic programming model. Furthermore, we will discuss how these aggregation methods can form the basis of an iterative solution approach.