Dealing with the inventory risk: a solution to the market making problem

@article{Guant2013DealingWT,
  title={Dealing with the inventory risk: a solution to the market making problem},
  author={Olivier Gu{\'e}ant and Charles-Albert Lehalle and Joaquin Fernandez-Tapia},
  journal={Mathematics and Financial Economics},
  year={2013},
  volume={7},
  pages={477-507}
}
Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we consider a stochastic control problem similar to the one introduced by Ho and Stoll (J Fin Econ 9(1): 47–73, 1981) and formalized mathematically by… 

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