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Financial scenario generation for stochastic multi-stage decision processes as facility location problems

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  • Ronald Hochreiter
  • Georg Pflug

Abstract

The quality of multi-stage stochastic optimization models as they appear in asset liability management, energy planning, transportation, supply chain management, and other applications depends heavily on the quality of the underlying scenario model, describing the uncertain processes influencing the profit/cost function, such as asset prices and liabilities, the energy demand process, demand for transportation, and the like. A common approach to generate scenarios is based on estimating an unknown distribution and matching its moments with moments of a discrete scenario model. This paper demonstrates that the problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function. We show that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance. The resulting optimization problem can be viewed as a multi-dimensional facility location problem, for which at least good heuristic algorithms exist. For multi-stage problems, a scenario tree is constructed as a nested facility location problem. Numerical convergence results for financial mean-risk portfolio selection conclude the paper. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Ronald Hochreiter & Georg Pflug, 2007. "Financial scenario generation for stochastic multi-stage decision processes as facility location problems," Annals of Operations Research, Springer, vol. 152(1), pages 257-272, July.
    • Handle: RePEc:spr:annopr:v:152:y:2007:i:1:p:257-272:10.1007/s10479-006-0140-6
    DOI: 10.1007/s10479-006-0140-6
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    1. Svetlozar T. Rachev & Werner Römisch, 2002. "Quantitative Stability in Stochastic Programming: The Method of Probability Metrics," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 792-818, November.
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    3. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
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    2. Yan, Rujing & Wang, Jiangjiang & Huo, Shuojie & Qin, Yanbo & Zhang, Jing & Tang, Saiqiu & Wang, Yuwei & Liu, Yan & Zhou, Lin, 2023. "Flexibility improvement and stochastic multi-scenario hybrid optimization for an integrated energy system with high-proportion renewable energy," Energy, Elsevier, vol. 263(PB).
    3. Zhe Yan & Zhiping Chen & Giorgio Consigli & Jia Liu & Ming Jin, 2020. "A copula-based scenario tree generation algorithm for multiperiod portfolio selection problems," Annals of Operations Research, Springer, vol. 292(2), pages 849-881, September.
    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. Barker, Andrew & Murray, Tim & Salerian, John, 2010. "Developing a Partial Equilibrium Model of an Urban Water System," Staff Working Papers 102, Productivity Commission, Government of Australia.
    6. Agnieszka Konicz & David Pisinger & Alex Weissensteiner, 2015. "Optimal annuity portfolio under inflation risk," Computational Management Science, Springer, vol. 12(3), pages 461-488, July.
    7. 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.
    8. D. Kuhn, 2009. "Convergent Bounds for Stochastic Programs with Expected Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 597-618, June.
    9. Yousaf Muhammad & Georg Pflug, 2014. "Stochastic vs deterministic programming in water management: the value of flexibility," Annals of Operations Research, Springer, vol. 223(1), pages 309-328, December.
    10. Sıtkı Gülten & Andrzej Ruszczyński, 2015. "Two-stage portfolio optimization with higher-order conditional measures of risk," Annals of Operations Research, Springer, vol. 229(1), pages 409-427, June.
    11. Backe, Stian & Ahang, Mohammadreza & Tomasgard, Asgeir, 2021. "Stable stochastic capacity expansion with variable renewables: Comparing moment matching and stratified scenario generation sampling," Applied Energy, Elsevier, vol. 302(C).
    12. Libo Yin & Liyan Han, 2020. "International Assets Allocation with Risk Management via Multi-Stage Stochastic Programming," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 383-405, February.
    13. Wang, Chengshan & Song, Guanyu & Li, Peng & Ji, Haoran & Zhao, Jinli & Wu, Jianzhong, 2017. "Optimal siting and sizing of soft open points in active electrical distribution networks," Applied Energy, Elsevier, vol. 189(C), pages 301-309.
    14. Wei Zhang & Kai Wang & Alexandre Jacquillat & Shuaian Wang, 2023. "Optimized Scenario Reduction: Solving Large-Scale Stochastic Programs with Quality Guarantees," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 886-908, July.
    15. Ekblom, J. & Blomvall, J., 2020. "Importance sampling in stochastic optimization: An application to intertemporal portfolio choice," European Journal of Operational Research, Elsevier, vol. 285(1), pages 106-119.
    16. Elçin Çetinkaya & Aurélie Thiele, 2016. "A moment matching approach to log-normal portfolio optimization," Computational Management Science, Springer, vol. 13(4), pages 501-520, October.
    17. Isha Chopra & Dharmaraja Selvamuthu, 2020. "Scenario generation in stochastic programming using principal component analysis based on moment-matching approach," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 190-201, March.
    18. Bhuvnesh Sharma & M. Ramkumar & Nachiappan Subramanian & Bharat Malhotra, 2019. "Dynamic temporary blood facility location-allocation during and post-disaster periods," Annals of Operations Research, Springer, vol. 283(1), pages 705-736, December.
    19. Angelos Georghiou & Daniel Kuhn & Wolfram Wiesemann, 2019. "The decision rule approach to optimization under uncertainty: methodology and applications," Computational Management Science, Springer, vol. 16(4), pages 545-576, October.
    20. Löhndorf, Nils, 2016. "An empirical analysis of scenario generation methods for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 255(1), pages 121-132.
    21. Ronald Hochreiter, 2009. "Evolutionary multi-stage financial scenario tree generation," Papers 0912.1534, arXiv.org, revised Jan 2010.
    22. Xiaoshi Guo & Sarah M. Ryan, 2021. "Reliability assessment of scenarios generated for stock index returns incorporating momentum," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4013-4031, July.
    23. Ponomareva, K. & Roman, D. & Date, P., 2015. "An algorithm for moment-matching scenario generation with application to financial portfolio optimisation," European Journal of Operational Research, Elsevier, vol. 240(3), pages 678-687.

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