Multi-Period Asset Allocation: An Application of Discrete Stochastic Programming

The issue of modeling farm financial decisions in a dynamic framework is addressed in this paper. Discrete stochastic programming is used to model the farm portfolio over the planning period. One of the main issues of discrete stochastic programming is representing the uncertainty of the data. The development of financial scenario generation routines provides a method to model the stochastic nature of the model. In this paper, two approaches are presented for generating scenarios for a farm portfolio problem. The approaches are based on copulas and optimization. The copula method provides an alternative to the multivariate normal assumption. The optimization method generates a number of discrete outcomes which satisfy specified statistical properties by solving a non-linear optimization model. The application of these different scenario generation methods is then applied to the topic of geographical diversification. The scenarios model the stochastic nature of crop returns and land prices in three separate geographic regions. The results indicate that the optimal diversification strategy is sensitive to both scenario generation method and initial acreage assumptions. The optimal diversification results are presented using both scenario generation methods.