The design of this study is to investigate the evolution of a stochastic price process consequent to discrete processes of bids and offers in a market microstructure setting. Under a set of flexible assumptions about agent preferences, we generate a price process to compare with observation. Specifically, we allow for both rational and irrational economic behavior, abstracting the inquiry from classical studies relying on utility theory. The goal is to provide a set of economic primitives which point inexorably to the price processes we see, rather than to assume such process from the start.
S. Hermannn and P. Imkeller, “The Exit Problem for Diffusions with Time Periodic Drift and Stochastic Resonance,” Prepublication No. 01, Institut de Mathématiques élie Cartan, Université Nancy 1, Lorraine, 2003.