Qing Zhang (U. of Georgia): 

Abstract:

Trading a financial asset involves a sequence of decisions to buy or sell the asset over time. A traditional trading strategy is to buy low and sell high. However, in practice, identifying these low and high levels is extremely challenging and difficult. In this talk, I will present our ongoing research on characterization of these key levels when the underlying asset price is dictated by a mean-reversion model. Our objective is to buy and sell the asset sequentially in order to maximize the overall profit. Mathematically, this amounts to determining a sequence of stopping times. We establish the associated dynamic programming equations (quasi-variational inequalities) and show that these differential equations can be converted to algebraic-like equations under certain conditions. The two threshold (buy and sell) levels can be found by solving these algebraic-like equations. We provide sufficient conditions that guarantee the optimality of our trading strategy. We also examine the dependence of these threshold levels on various parameters in numerical examples.