具有完全状态依赖序动力学的限价订单簿模型的弱大数定律
A weak law of large numbers for a limit order book model with fully state dependent order dynamics
摘要：
研究了一个限价订单簿模型，其中订单动态同时依赖于当前最优价格和当前交易量密度函数。对于最佳买价、最佳卖价和LOB两侧的成交量密度的联合动态，我们推导出一个弱大数定律，该定律指出，当单个订单的大小以及最小价格变动单位趋于零且订单到达率趋于无穷大时，LOB模型收敛到连续时间极限。在比例限制下，两个体积密度都遵循一个非线性偏微分方程和两个描述最佳出价和卖价的非线性常微分方程。
英文摘要：
This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and the standing volume densities on both sides of the LOB we derive a weak law of large numbers, which states that the LOB model converges to a continuous-time limit when the size of an individual order as well as the tick size tend to zero and the order arrival rate tends to infinity. In the scaling limit the two volume densities follow each a non-linear PDE coupled with two non-linear ODEs that describe the best bid and ask price.
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