Aggregation and Discretization in Multistage Stochastic Programming

This research project deals with repeated decision problems under uncertainty which can be formulated as multistage stochastic programs (MSPs). Without any suitable approximations, such problems can usually not be solved, neither analytically nor numerically. Thus, the principal objective of this project is the development and validation of a universal stage aggregation and scenario generation scheme which applies to a broad class of MSPs. Error bounds and convergence properties will be thoroughly investigated. Further emphasis is put on the formulation of weak regularity conditions under which the new approximation scheme is applicable. As far as discretization of time and (probability) space is concerned, the tradeoff between temporal and spacial resolution will be assessed.

The new approximation method is applied to the valuation of electricity derivatives (e.g. swing options) and some other prototypical real-life decision problems in the energy and finance sectors.