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Title Scenario Tree Generation by Optimal Discretization
Author Sigurbjörnsson, Sigurdur Rafnar Sigurbjörnsson
Supervisor Clausen, Jens (Operations Research, Department of Manufacturing Engineering and Management, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2008
Abstract Scenario tree generation is an important step in stochastic optimization. The methods for scenario tree generation are often problem specific and no one best solution exists. Recent approaches suggested by Pug and Hochreiter solve the problem by generating a scenario tree by minimizing a probability metric between a tree structure and a sample of a stochastic process. Their results are interesting and indicate stability of the objective value. The purpose of this thesis is to become acquainted with scenario tree generation by optimal discretization and to study the stability of such scenario trees with focus on the rst stage solution in a multivariate multi-stage problems. A vector autoregression model is fitted to time series for the term structure of the Danish bond market and the OMXC20 index. Scenario paths are sampled by minimizing a probability metric between the tree and the sample paths. The stability of the generated scenario trees is studied in a ve stage ALM problem. The numerical results for the ALM problem indicate that the first stage solution for scenario trees generated by the optimal discretization method, of the sizes tested here, are not stable.
Series IMM-M.Sc.-2008-67
Fulltext
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Admin Creation date: 2008-09-10    Update date: 2008-11-13    Source: dtu    ID: 223396    Original MXD