Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Speaker: Tomoyuki Ichiba, University of California, Santa Barbara

ABSTRACT

In this talk we examine the colliding behavior of Brownian particles which diffuse on the real line determined by a class of stochastic differential equations. The absence and the presence of triple (or higher order) collisions among the particles are crucial in analysis of local time processes accumulated by these collisions. Especially, this analysis sheds light on some important characteristics (e.g., identification, solvability, time-reversal, invariant distributions) of the stochastic system with piece-wise constant or degenerate coefficients. As a case study, we discuss portfolios under a financial equity market model with rank-based characteristics.