||Scenario Tree Generation by Optimal Discretization
||Sigurbjörnsson, Sigurdur Rafnar Sigurbjörnsson
||Clausen, Jens (Operations Research, Department of Manufacturing Engineering and Management, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||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.
Creation date: 2008-09-10
Update date: 2008-11-13