Date of Award

Spring 2015

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Statistics

First Advisor

Frederi G. Viens

Committee Chair

Frederi G. Viens

Committee Member 1

Fabrice Baudoin

Committee Member 2

Hao Zhang

Committee Member 3

Jose E. Figueroa-Lopez

Abstract

We propose a new market-making model which incorporates a number of realistic features relevant for high-frequency trading. In particular, we model the dependency structure of prices and order arrivals with novel self- and cross-exciting point processes. Furthermore, instead of assuming the bid and ask prices can be adjusted continuously by the market maker, we formulate the market maker's decisions as an optimal switching problem. Moreover, the risk of overtrading has been taken into consideration by allowing each order to have different size, and the market maker can make use of market orders, which are treated as impulse control, to get rid of excessive inventory. Because of the stochastic intensities of the cross-exciting point processes, the optimality condition cannot be formulated using classical Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI), so we extend the framework of constrained forward backward stochastic differential equation (CFBSDE) to solve our optimal control problem.

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