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In this paper we extend the market-making models with inventory constraints of Avellaneda and Stoikov ("High-frequency trading in a limit-order book", Quantitative Finance Vol.8 No.3 2008) and Gueant, Lehalle and Fernandez-Tapia ("Dealing with inventory risk", Preprint 2011) to the case of a rather general class of mid-price processes, under either exponential or linear PNL utility functions, and we add an inventory-risk-aversion parameter that penalises the marker-maker if she finishes her day with a non-zero inventory.
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Fleming, Soner (2006) Controlled Markov processes and viscosity solutions . Springer
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Cited alongside, same era.
Avellaneda, Stoikov (2008) High-frequency trading in a limit-order book . Quantitative Finance Vol. 8 No. 3
2008
Cited alongside, same era.
Pham (2009) Continuous-time stochastic control and optimization with financial applications . Springer
2009
Cited alongside, same era.
Cartea, Jaimungai (2011) Buy Low Sell High: A High Frequency Trading Perspective . Preprint SSRN
2011
Cited alongside, same era.
Guéant, Lehalle, Fernández-Tapia (2011) Dealing with inventory risk . Preprint
2011
Later among the works it cites.
Guilbaud, Pham (2011) Optimal high frequency trading with limit and market orders . Preprint, to appear in Quantitative Finance
2011
Later among the works it cites.
Cartea, Jaimungai (2012) Risk Measures and Fine Tuning of High Frequency Trading Strategies . Preprint SSRN
2012
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