Mathematical Models of Trading

This thesis presents a mathematical framework to model trading of financial assets on an exchange. The interaction between agents on the exchange is modeled as the Nash equilibrium of a demand schedule auction. The submission of demand schedules in the auction is meant to proxy for the submission of limit and market orders on an exchange. Chapter 1 considers this auction in a one-period setting, highlighting the importance of noisy flow for obtaining a unique Nash equilibrium. Chapter 2 is the core of the thesis and considers the auction in a continuous time setting. Here the agents trading on the exchange have quadratic-type preferences, and in equilibrium they must clear an exogenously specified stream of market orders. Chapter 3 considers alternative and more realistic dynamics for the exogenous market orders. Chapter 4 endogenizes the market orders by considering an agent executing orders on behalf of noisy clients.. Chapter 5 considers the same model as in Chapter 2, except with a consumption based utility function for each agent.