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Discretized reality and spurious profits in stochastic programming models for asset/liability management

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  • Klaassen, Pieter

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

Abstract

In the literature on stochastic programming models for practical portfolio investment problems, relatively little attention has been devoted to the question how the necessarily approximate description of the asset-price uncertainty in these models influences the optimal solution. In this paper we will show that it is important that asset prices in such a description are arbitrage-free. Descriptions which have been suggested in the literature are often inconsistent with observed market prices and/or use sampling to obtain a set of scenarios about the future. We will show that this effectively introduces arbitrage opportunities in the optimization model. For an investor who cannot exploit arbitrage opportunities directly because of market imperfections and trading restrictions, we will illustrate that the presence of such arbitrage opportunities may cause substantial biases in the optimal investment strategy.

Suggested Citation

  • 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.
    • Handle: RePEc:vua:wpaper:1997-11
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    Cited by:

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    3. 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.
    4. Weissensteiner, Alex, 2010. "Using the Black-Derman-Toy interest rate model for portfolio optimization," European Journal of Operational Research, Elsevier, vol. 202(1), pages 175-181, April.
    5. Sodhi, ManMohan S. & Tang, Christopher S., 2009. "Modeling supply-chain planning under demand uncertainty using stochastic programming: A survey motivated by asset-liability management," International Journal of Production Economics, Elsevier, vol. 121(2), pages 728-738, October.
    6. Mitra, Sovan & Lim, Sungmook & Karathanasopoulos, Andreas, 2019. "Regression based scenario generation: Applications for performance management," Operations Research Perspectives, Elsevier, vol. 6(C).
    7. Pieter Klaassen, 2002. "Comment on "Generating Scenario Trees for Multistage Decision Problems"," Management Science, INFORMS, vol. 48(11), pages 1512-1516, November.
    8. 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.
    9. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2010. "No-arbitrage conditions, scenario trees, and multi-asset financial optimization," European Journal of Operational Research, Elsevier, vol. 206(3), pages 609-613, November.
    10. de Lange, Petter E. & Fleten, Stein-Erik & Gaivoronski, Alexei A., 2004. "Modeling financial reinsurance in the casualty insurance business via stochastic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 991-1012, February.
    11. Rocha, Paula & Kuhn, Daniel, 2012. "Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules," European Journal of Operational Research, Elsevier, vol. 216(2), pages 397-408.
    12. Barro, Diana & Consigli, Giorgio & Varun, Vivek, 2022. "A stochastic programming model for dynamic portfolio management with financial derivatives," Journal of Banking & Finance, Elsevier, vol. 140(C).
    13. M. Schyns & Y. Crama & G. Hübner, 2010. "Optimal selection of a portfolio of options under Value-at-Risk constraints: a scenario approach," Annals of Operations Research, Springer, vol. 181(1), pages 683-708, December.
    14. ManMohan S. Sodhi, 2005. "LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications," Operations Research, INFORMS, vol. 53(2), pages 181-196, April.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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