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Complete markets do not allow free cash flow streams

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  • Nicole Bäuerle
  • Stefanie Grether

Abstract

In this short note we prove a conjecture posed in Cui et al. (Math Finance 22:346–378, 2012 ): Dynamic mean–variance problems in arbitrage-free, complete financial markets do not allow free cash flows. Moreover, we show by investigating a benchmark problem that this effect is due to the performance criterion and not due to the time inconsistency of the strategy. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Nicole Bäuerle & Stefanie Grether, 2015. "Complete markets do not allow free cash flow streams," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 137-146, April.
    • Handle: RePEc:spr:mathme:v:81:y:2015:i:2:p:137-146
    DOI: 10.1007/s00186-014-0489-2
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    Cited by:

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    2. Aleš Černý, 2020. "Semimartingale theory of monotone mean–variance portfolio allocation," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1168-1178, July.
    3. Yang Shen & Bin Zou, 2022. "Cone-constrained Monotone Mean-Variance Portfolio Selection Under Diffusion Models," Papers 2205.15905, arXiv.org.
    4. Jakub Trybuła & Dariusz Zawisza, 2019. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 966-987, August.
    5. Alev{s} v{C}ern'y, 2019. "Semimartingale theory of monotone mean--variance portfolio allocation," Papers 1903.06912, arXiv.org, revised Jan 2020.
    6. Peter A. Forsyth & Kenneth R. Vetzal, 2017. "Dynamic mean variance asset allocation: Tests for robustness," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-37, June.
    7. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
    8. Yuchen Li & Zongxia Liang & Shunzhi Pang, 2022. "Continuous-Time Monotone Mean-Variance Portfolio Selection in Jump-Diffusion Model," Papers 2211.12168, arXiv.org, revised May 2024.
    9. Dang, D.M. & Forsyth, P.A., 2016. "Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach," European Journal of Operational Research, Elsevier, vol. 250(3), pages 827-841.
    10. Peter A. Forsyth & George Labahn, 2017. "$\epsilon$-Monotone Fourier Methods for Optimal Stochastic Control in Finance," Papers 1710.08450, arXiv.org, revised Apr 2018.
    11. Nicole Bäuerle & Tamara Göll, 2023. "Nash equilibria for relative investors via no-arbitrage arguments," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 1-23, February.

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