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A model for a large investor trading at market indifference prices. II: Continuous-time case

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  • Peter Bank
  • Dmitry Kramkov

Abstract

We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the investor's orders and trade among themselves to attain Pareto optimal allocations. We first consider the case of simple strategies and then, in analogy to the construction of stochastic integrals, investigate the transition to general continuous dynamics. As a result, we show that the model's evolution can be described by a nonlinear stochastic differential equation for the market makers' expected utilities.

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  • Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. II: Continuous-time case," Papers 1110.3229, arXiv.org, revised Sep 2015.
    • Handle: RePEc:arx:papers:1110.3229
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    7. Peter Bank & Dmitry Kramkov, 2013. "The stochastic field of aggregate utilities and its saddle conjugate," Papers 1310.7280, arXiv.org.
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    16. Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. I: single-period case," Papers 1110.3224, arXiv.org, revised Dec 2013.
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    Citations

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    Cited by:

    1. Masaaki Fukasawa, 2014. "Efficient price dynamics in a limit order market: an utility indifference approach," Papers 1410.8224, arXiv.org.
    2. Peter Bank & Selim Gökay, 2016. "Superreplication when trading at market indifference prices," Finance and Stochastics, Springer, vol. 20(1), pages 153-182, January.
    3. Grigorova, Miryana & Quenez, Marie-Claire & Sulem, Agnès, 2021. "American options in a non-linear incomplete market model with default," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 479-512.
    4. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2017. "American options in an imperfect market with default," Papers 1708.08675, arXiv.org.
    5. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    6. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2019. "Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve Modeling," Post-Print hal-01721441, HAL.
    7. Thai Nguyen & Mitja Stadje, 2020. "Utility maximization under endogenous pricing," Papers 2005.04312, arXiv.org, revised Mar 2024.
    8. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "European options in a non-linear incomplete market model with default," Working Papers hal-02025833, HAL.
    9. Ibrahim Ekren & Sergey Nadtochiy, 2019. "Utility-based pricing and hedging of contingent claims in Almgren-Chriss model with temporary price impact," Papers 1910.01778, arXiv.org, revised Jun 2020.
    10. Masaaki Fukasawa & Mitja Stadje, 2018. "Perfect hedging under endogenous permanent market impacts," Finance and Stochastics, Springer, vol. 22(2), pages 417-442, April.
    11. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "American options in a non-linear incomplete market model with default," Working Papers hal-02025835, HAL.
    12. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2021. "American options in a non-linear incomplete market model with default," Post-Print hal-02025835, HAL.
    13. Peter Bank & Dmitry Kramkov, 2015. "A model for a large investor trading at market indifference prices. I: Single-period case," Finance and Stochastics, Springer, vol. 19(2), pages 449-472, April.
    14. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2020. "European options in a non-linear incomplete market model with default," Post-Print hal-02025833, HAL.
    15. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2018. "Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve Modeling," Working Papers hal-01721441, HAL.

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