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Stability of Radner equilibria with respect to small frictions

Author

Listed:
  • Martin Herdegen

    (University of Warwick)

  • Johannes Muhle-Karbe

    (Carnegie Mellon University)

Abstract

We study risk-sharing equilibria with trading subject to small proportional transaction costs. We show that the frictionless equilibrium prices also form an “asymptotic equilibrium” in the small-cost limit. More precisely, there exist asymptotically optimal policies for all agents and a split of the trading cost according to their risk aversions for which the frictionless equilibrium prices still clear the market. Starting from a frictionless equilibrium, this allows studying the interplay of volatility, liquidity and trading volume.

Suggested Citation

  • Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-018-0354-x
    DOI: 10.1007/s00780-018-0354-x
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    Citations

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    Cited by:

    1. Bouchard, Bruno & Muhle-Karbe, Johannes, 2022. "Simple bounds for utility maximization with small transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 98-113.
    2. Xiaofei Shi & Daran Xu & Zhanhao Zhang, 2021. "Deep Learning Algorithms for Hedging with Frictions," Papers 2111.01931, arXiv.org, revised Dec 2022.
    3. Jin Hyuk Choi & Jetlir Duraj & Kim Weston, 2023. "A multi-agent targeted trading equilibrium with transaction costs," Papers 2306.08519, arXiv.org.
    4. Herdegen, Martin & Muhle-Karbe, Johannes, 2019. "Sensitivity of optimal consumption streams," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1964-1992.
    5. Xiaofei Shi & Daran Xu & Zhanhao Zhang, 2023. "Deep learning algorithms for hedging with frictions," Digital Finance, Springer, vol. 5(1), pages 113-147, March.
    6. Erhan Bayraktar & Thomas Cayé & Ibrahim Ekren, 2021. "Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 36-108, January.
    7. Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2018. "Equilibrium returns with transaction costs," Finance and Stochastics, Springer, vol. 22(3), pages 569-601, July.
    8. Eunjung Noh & Kim Weston, 2020. "Price impact equilibrium with transaction costs and TWAP trading," Papers 2002.08286, arXiv.org.
    9. Cayé, Thomas & Herdegen, Martin & Muhle-Karbe, Johannes, 2020. "Scaling limits of processes with fast nonlinear mean reversion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1994-2031.
    10. Isaenko, Sergey, 2023. "Transaction costs, frequent trading, and stock prices," Journal of Financial Markets, Elsevier, vol. 64(C).

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    More about this item

    Keywords

    Trading costs; Radner equilibrium; Asymptotics; Stability; Transaction tax;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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