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Hedging, arbitrage and optimality with superlinear frictions

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  • Paolo Guasoni
  • Mikl'os R'asonyi

Abstract

In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality between feasible trading strategies and shadow execution prices with a martingale measure. Utility maximizing strategies exist even if arbitrage is present, because it is not scalable at will.

Suggested Citation

  • Paolo Guasoni & Mikl'os R'asonyi, 2015. "Hedging, arbitrage and optimality with superlinear frictions," Papers 1506.05895, arXiv.org.
    • Handle: RePEc:arx:papers:1506.05895
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    References listed on IDEAS

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    Cited by:

    1. Xiaofei Shi & Daran Xu & Zhanhao Zhang, 2021. "Deep Learning Algorithms for Hedging with Frictions," Papers 2111.01931, arXiv.org, revised Dec 2022.
    2. Huy N. Chau & Mikl'os R'asonyi, 2016. "Skorohod's representation theorem and optimal strategies for markets with frictions," Papers 1606.07311, arXiv.org, revised Apr 2017.
    3. Paolo Guasoni & Marko H. Weber, 2018. "Rebalancing Multiple Assets with Mutual Price Impact," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 618-653, November.
    4. Lukas Gonon & Johannes Muhle-Karbe & Xiaofei Shi, 2019. "Asset Pricing with General Transaction Costs: Theory and Numerics," Papers 1905.05027, arXiv.org, revised Apr 2020.
    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. Peter Bank & Selim Gökay, 2016. "Superreplication when trading at market indifference prices," Finance and Stochastics, Springer, vol. 20(1), pages 153-182, January.
    8. Teemu Pennanen & Ari-Pekka Perkkio, 2016. "Convex duality in optimal investment and contingent claim valuation in illiquid markets," Papers 1603.02867, arXiv.org.
    9. Peter Bank & Yan Dolinsky, 2018. "Continuous-time Duality for Super-replication with Transient Price Impact," Papers 1808.09807, arXiv.org, revised May 2019.
    10. Erindi Allaj, 2017. "Implicit Transaction Costs And The Fundamental Theorems Of Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-39, June.
    11. Yan Dolinsky, 2022. "Duality Theory for Exponential Utility--Based Hedging in the Almgren--Chriss Model," Papers 2210.03917, arXiv.org, revised Jun 2023.
    12. Yan Dolinsky & Doron Greenstein, 2024. "A Note on Optimal Liquidation with Linear Price Impact," Papers 2402.14100, arXiv.org.

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