This dissertation contains three essays that explore various topics in market microstructure and asset pricing. These topics include statistical arbitrage, algorithmic trading, market manipulation, and term-structure modeling.

Chapter 1 studies a model of statistical arbitrage trading in an environment with fat-tailed information. I show that if risk-neutral arbitrageurs are uncertain about the variance of fat-tail shocks and if they implement max-min robust optimization, they will choose to ignore a wide range of pricing errors. Although model risk hinders their willingness to trade, arbitrageurs can capture the most profitable opportunities because they follow a linear momentum strategy beyond the inaction zone. This is exactly equivalent to a famous machine-learning algorithm called LASSO. Arbitrageurs can also amass market power due to their conservative trading under this strategy. Their uncoordinated exercise of robust control facilitates tacit collusion, protecting their profits from being competed away even if their number goes to infinity. This work sheds light on how algorithmic trading by arbitrageurs may adversely affect the competitiveness and efficiency of financial markets.

Chapter 2 extends the basic model in Chapter 1 by considering an insider who strategically interacts with a group of algorithmic arbitrageurs who follow machine-learning-type trading strategies. When market liquidity is good enough, arbitrageurs may be induced to trade too aggressively, giving the insider a reversal trading opportunity. In this case, the insider may play a pump-and-dump strategy to trick those arbitrageurs. This strategy is very similar to those controversial trading practices (such as momentum ignition and stop-loss hunting) in reality. We show that such strategies can largely distort price informativeness and threaten market stability at the expense of common investors. This study reveals a list of economic conditions under which this type of trade-based manipulations are likely to occur. Policy implications are discussed as well.

Chapter 3 provides a simple proof for the long-run pricing kernel decomposition developed by Hansen and Scheinkman (Econometrica, 2009). In a stationary Markovian economy, the long forward rate should be flat so that the pricing kernel can be easily factorized in a multiplicative form of the transitory and permanent components. The permanent (martingale) component plays a key role as it induces the change of probabilities to the long forward measure where the long-maturity discount bond serves as the numeraire. I derive an explicit expression for this martingale component. It reveals a strong restriction on the market prices of risk in a popular approach of interest rates modeling. This approach neglects the permanent martingale component and restricts risk premia in a way undesirable for model calibration. Further analysis demonstrates the advantages of equilibrium modeling of a production economy since it is featured with a path-dependent pricing kernel that has a non-degenerate permanent martingale.