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Comment on "Generating Scenario Trees for Multistage Decision Problems"

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  • Pieter Klaassen

    (Department of Finance and Financial Sector Management, Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands)

Abstract

In models of decision making under uncertainty, one typically has to approximate the uncertainties by a limited number of discrete outcomes. Høyland and Wallace (2001) formulate a nonlinear programming problem to generate such a limited number of discrete outcomes while satisfying specified statistical properties. They have developed and employed this method for a stochastic multistage asset-allocation problem. When the method is applied to such financial optimization problems under uncertainty, we argue here that it does not suffice to match statistical properties. To obtain realistic outcomes, the (limited) description of the uncertainty in such models should also exclude arbitrage opportunities, and thereby be consistent with financial asset pricing theory. We illustrate that the method proposed by Høyland and Wallace can result in arbitrage opportunities in the scenario tree if only statistical properties are imposed. We show how one can check ex post for the presence of arbitrage opportunities in a scenario tree by checking for the existence of solutions to sets of linear equations. Arbitrage opportunities can also be precluded ex ante in the scenario tree by adding constraints to the nonlinear programming problem of Høyland and Wallace.

Suggested Citation

  • Pieter Klaassen, 2002. "Comment on "Generating Scenario Trees for Multistage Decision Problems"," Management Science, INFORMS, vol. 48(11), pages 1512-1516, November.
    • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:11:p:1512-1516
    DOI: 10.1287/mnsc.48.11.1512.261
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    References listed on IDEAS

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    1. Gondzio, Jacek & Kouwenberg, Roy & Vorst, Ton, 2003. "Hedging options under transaction costs and stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1045-1068, April.
    2. Kouwenberg, Roy, 2001. "Scenario generation and stochastic programming models for asset liability management," European Journal of Operational Research, Elsevier, vol. 134(2), pages 279-292, October.
    3. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
    4. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," Serie Research Memoranda 0011, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    5. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," European Journal of Operational Research, Elsevier, vol. 101(2), pages 374-392, September.
    6. Pieter Klaassen, 1998. "Financial Asset-Pricing Theory and Stochastic Programming Models for Asset/Liability Management: A Synthesis," Management Science, INFORMS, vol. 44(1), pages 31-48, January.
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    Cited by:

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    2. Libo Yin & Liyan Han, 2013. "Options strategies for international portfolios with overall risk management via multi-stage stochastic programming," Annals of Operations Research, Springer, vol. 206(1), pages 557-576, July.
    3. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "A dynamic stochastic programming model for international portfolio management," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1501-1524, March.
    4. Staino, Alessandro & Russo, Emilio, 2015. "A moment-matching method to generate arbitrage-free scenarios," European Journal of Operational Research, Elsevier, vol. 246(2), pages 619-630.
    5. Robert Ferstl & Alex Weissensteiner, 2010. "Cash management using multi-stage stochastic programming," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 209-219.
    6. Davari-Ardakani, Hamed & Aminnayeri, Majid & Seifi, Abbas, 2014. "A study on modeling the dynamics of statistically dependent returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 35-51.
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    8. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2014. "No-Arbitrage ROM simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 66-79.
    9. Consiglio, Andrea & Carollo, Angelo & Zenios, Stavros A., 2014. "Generating Multi-factor Arbitrage-Free Scenario Trees with Global Optimization," Working Papers 13-35, University of Pennsylvania, Wharton School, Weiss Center.
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