In this thesis, problems in the realm of high frequency trading and optimal market making are established and solved in both single asset and multiple asset economies. For an agent that is averse to holding large inventories for long periods of time, optimal high frequency trading strategies are...

In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (online store). This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in order to maximize her...

The problems caused by state and local revenue volatility are inherently challenging. The State of Oregon has an especially volatile revenue structure, which can cause all sorts of problems as the state moves through the business cycle. Nevertheless, we have concluded that these problems are...

We consider the optimal strategy of R&D expenditure adopted by a firm that engages in R&D to develop an innovative product to be launched in the market. The firm faces with technological uncertainty associated with the success of the R&D effort and market uncertainty of the stochastic revenue...

We present a two-armed bandit model of decision making under uncertainty where the expected return to investing in the "risky arm'' increases when choosing that arm and decreases when choosing the "safe'' arm. These dynamics are natural in applications such as human capital development, job...

We present efficient partial differential equation (PDE) methods for continuous time mean-variance portfolio allocation problems when the underlying risky asset follows a jump-diffusion. The standard formulation of mean-variance optimal portfolio allocation problems, where the total wealth is...