Quotation Geyer, Alois, Hanke, Michael, Weissensteiner, Alex. 2010. No-arbitrage conditions, scenario trees, and multi-asset financial optimization. European Journal of Operational Research (EJOR) 206 (3): 609-613.




Many numerical optimization methods use scenario trees as a discrete approximation for the true (multi-dimensional) probability distributions of the problem's random variables. Realistic specifications in financial optimization models can lead to tree sizes that quickly become computationally intractable. In this paper we focus on the two main approaches proposed in the literature to deal with this problem: scenario reduction and state aggregation. We first state necessary conditions for the node structure of a tree to rule out arbitrage. However, currently available scenario reduction algorithms do not take these conditions explicitly into account. State aggregation excludes arbitrage opportunities by relying on the risk-neutral measure. This is, however, only appropriate for pricing purposes but not for optimization. Both limitations are illustrated by numerical examples. We conclude that neither of these methods is suitable to solve financial optimization models in asset liability or portfolio management.


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal European Journal of Operational Research (EJOR)
Citation Index SCI
WU Journalrating 2009 A
WU-Journal-Rating new FIN-A, INF-A, STRAT-A, VW-B, WH-A
Language English
Title No-arbitrage conditions, scenario trees, and multi-asset financial optimization
Volume 206
Number 3
Year 2010
Page from 609
Page to 613
URL http://dx.doi.org/10.1016/j.ejor.2010.03.022


Stochastic optimization of multi-period asset allocation problems
Geyer, Alois (Details)
Hanke, Michael (Former researcher)
Weissensteiner, Alex (Universität Innsbruck)
Institute for Financial Research IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1121 Operations research (Details)
5361 Financial management (Details)
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