9,811 research outputs found

    Evolutionary multi-stage financial scenario tree generation

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    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 this paper, a new evolutionary algorithm to create scenario trees for multi-stage financial optimization models will be presented. Numerical results and implementation details conclude the paper

    Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring

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    We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can be 2-colored in a way that results in few changes between any two consecutive layers. This approach follows the framework of multistage problems that has received a growing amount of attention in recent years. We investigate the complexity of recognizing these graphs. We show that this problem is NP-hard even if there are only two layers or if only one change is allowed between consecutive layers. We consider the parameterized complexity of the problem with respect to several structural graph parameters, which we transfer from the static to the temporal setting in three different ways. Finally, we consider a version of the problem in which we only restrict the total number of changes throughout the lifetime of the graph. We show that this variant is fixed-parameter tractable with respect to the number of changes
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