<p> This dissertation consists of two topics. In chapter 1, we develop a discrete disaggregated model in which, the market maker can observe individual order flow instead of a batch order in Kyle (1985). The model suggests that the behavior of the uninformed traders play an important role in how the informed make the optimal trading strategy : when the uninformed is more likely to use large order, the informed will also trade large, no matter what size of signal he receives, and when the uninformed tend to trade with small size order, the informed will have to trade small quantity to maximize his expected profit, even if he receives the large value signal. When the uninformed does not prefer size of order, the informed will trade smaller (larger) quantities when receiving small(large) value signals. The result is consistent with the behavior of the informed in Kyle (1985). We further investigate order flow disaggregation on market liquidity by comparing aggregated order flow structure, in which market maker observes aggregated order flow. When the model setup is symmetric, the aggregated structure can provide more liquidity, while the disaggregated structure is more liquid under the asymmetric model setup. In chapter 2, we employ the type 2 joint power law distribution in Mardia (1962) to study the joint effect of the return and trading volume. The parameter estimate for marginal distribution in joint power-law exhibits the same pattern as in univariate power law literature for return and volume, but the value are smaller due to the joint effect of return and trading volume. However, we find the joint power law shows higher predictability than the univariate power law by employing the measure MSE (Means squared error). Additionally, the type 2 joint power law indicates the linear relationship between log absolute value of return and log trading volume , which suggests the none linear impact of trading volume on price. We also find that, as sampling interval shrinks from day to 15 seconds, the price impact will increase. And also as the waiting time for two consecutive transactions shrinks, the price impact will increase, which is in line with the result of Dufour and Engle (2000). </p>