A copula-based heuristic for scenario generation

In most practical applications of stochastic programming, we have to approximate the probability distribution of the stochastic parameters by a discrete distribution, i.e. a list of realizations (scenarios) and their probabilities. The process of generating this discrete distribution is usually referred to as ‘scenario generation’. As with any other approximation, the quality of the scenarios is an important determinant of the quality of the solutions obtained from the model—bad scenarios can ruin an otherwise Wawless model. This issue is further complicated by the fact that we typically want to keep the number of scenarios as low as possible, to be able to solve the problem in a reasonable time. There are many methods for generating scenarios, see Dupačová et al. (2000) for an overview. Some of these methods try to generate scenarios that match a given set of speciVcations for their marginal distributions and the dependence between them, where the latter is almost always speciVed using the correlation (or variance-covariance) matrix. This is suXcient for elliptical distributions such as normal or the Student’s t-distribution, but might fail in the general case: it cannot, for example, model asymmetric dependence (a situation where the dependence in down-turns diUers from the up-turns) or tail dependence—phenomena known to exist in Vnancial data (Hu, 2006; Longin and Solnik, 2001; Patton, 2002, 2004), or industries with changing trends, such as the apparel industry (Vaagen and Wallace, 2008).