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On a stochastic differential equation arising in a price impact model

Author

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  • Bank, Peter
  • Kramkov, Dmitry

Abstract

We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in the price impact model developed by Bank and Kramkov (2011) [1,2]. These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments.

Suggested Citation

  • Bank, Peter & Kramkov, Dmitry, 2013. "On a stochastic differential equation arising in a price impact model," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1160-1175.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:3:p:1160-1175
    DOI: 10.1016/j.spa.2012.10.011
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    Cited by:

    1. 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.
    2. 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.
    3. Peter Bank & Dmitry Kramkov, 2013. "The stochastic field of aggregate utilities and its saddle conjugate," Papers 1310.7280, arXiv.org.

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