RT
LZ刚刚接触金融工程，最近在读大神paper时有点困惑，想问一下论坛里的各位大神。。。
文章是High-frequency trading in a limit order book, Macro Avellaneda写的，发在Quantitative Finance上
文章链接：http://xueshu.baidu.com/s?wd=pap ... 3123242556029463449

文章说明了假设股票价格符合简单布朗运动
“dSu =σ
dWu
with initial value St = s. Here Wt is a standard onedimensional Brownian motion and
is constant.Underlying this continuous-time model is the implicit assumption that our agent has no opinion on the drift or any autocorrelation structure for the stock. ”  

然后文章假设投资者在t时刻的价值函数类似常数绝对风险厌恶效用函数(CARA)，为

其中，x是投资者的cash，q是投资者的股票数，γ是参数。
“We first model an inactive trader who does not have any limit orders in the market and simply holds an inventory of q stocks until the terminal time T. This ‘frozen inventory’ strategy will later prove to be useful in the case when limit orders are allowed.”
“x is the initial wealth in dollars”


到这里都还OK，然后作者应该是用了布朗运动的期望性质（个人猜测），就把公式改写成了这样

请问这个是为什么啊我推了半天没有推出来。。。有没有大神知道的

先谢谢各位大神