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. This general,
non-martingale framework allows a market-maker to make directional bets on
market trends whilst keeping under control her inventory risk. In order to
achieve this, the marker-maker places non-symmetric limit orders that favour
market orders to hit her bid (resp. ask) quotes if she expects that prices will
go up (resp. down).
With this inventory-risk-aversion parameter, the market-maker has not only
direct control on her inventory risk but she also has indirect control on the
moments of her PNL distribution. Therefore, this parameter can be seen as a
fine-tuning of the marker-maker's risk-reward profile.
In the case of a mean-reverting mid-price, we show numerically that the
inventory-risk-aversion parameter gives the market-maker enough room to tailor
her risk-reward profile, depending on her risk budgets in inventory and PNL
distribution (especially variance, skewness, kurtosis and VaR). For example,
when compared to the martingale benchmark, a market can choose to either
increase her average PNL by more than 15% and carry a huge risk, on inventory
and PNL, or either give up 5% of her benchmark PNL to increase her control on
inventory and PNL, as well as increasing her Sharpe ratio by a factor bigger
than 2.

在这篇论文中，我们将存货约束市场制作模型扩展到了相当一般的中间价格过程情况，针对指数或线性 PNL 效用函数，添加了一个存货风险规避参数，这个参数可以看作是市场制造者风险回报配置的微调。