A framework for the reduction of scenario trees as inputs of (linear) multistage stochastic programs is provided such that optimal values and approximate solution sets remain close to each other. The argument is based on upper bounds of the Lr -distance and the filtration distance, and on quantitative stability results for multistage stochastic programs. The important difference from scenario r...

An important issue for solving multistage stochastic programs consists in the approximate representation of the (multivariate) stochastic input process in the form of a scenario tree. In this paper, forward and backward approaches are developed for generating scenario trees out of an initial fan of individual scenarios. Both approaches are motivated by the recent stability result in [15] for op...

An important issue for solving multistage stochastic programs consists in the approximate representation of the (multivariate) stochastic input process in the form of a scenario tree. In this paper, we develop (stability) theory-based heuristics for generating scenario trees out of an initial set of scenarios. They are based on forward or backward algorithms for tree generation consisting of re...

Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations (represented as scenario trees) have been suggested in the literature. In th...

Sometimes, the best available information about an uncertain future is a single forecast. On the other hand, stochastic-programming models need future data in the form of scenario trees. While a single forecast does not provide enough information to construct a scenario tree, a forecast combined with historical data does—but none of the standard scenario-generation methods is suited to handle t...

In stochastic programming and decision analysis, an important issue consists in the approximate representation of the multidimensional stochastic underlying process in the form of scenario tree. This paper presents the approach to generate the multistage multidimensional scenario tree out of a set of scenario fans. For this purpose, the multistage K-means clustering algorithm is developed. The ...

In this paper we present our ideas for conducting a cost benefit analysis by using three different methods: scenario analysis, decision trees and simulation. Then we introduce our case study and examine these methods in a real world situation. We show how these tools can be used and what the results are for each of them. Our aim is to conduct a comparison of these different probabilistic method...

Several concepts have been used to describe potential serous accidents in industrial activities. Examples of these concepts are worst case scenarios, likelier-but-less-catastrophic scenarios, most credible scenarios etc. A worst case scenario is a sequence of events/actions/accidents for a certain place (site) and time which causes the worst magnitude of an accident. Often these kind of acciden...

Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis ...