Dr. Mykhaylo Shkolnikov (University of California, Berkeley)

Title: Asymmetrically colliding Brownian particles in stochastic portfolio theory and beyond

Abstract:We will discuss systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. These can be identified with the collections of ordered processes in a Brownian particle system, in which the drift coefficients, the diffusion coefficients, and the collision local times for the individual particles are assigned according to their ranks. Such processes can be viewed as generalizations of those arising in first-order models for equity markets in the context of stochastic portfolio theory, and are able to correct for several shortcomings of such models while being equally amenable to computations. We also show that, in addition to being of interest in their own right, such systems of Brownian particles arise as universal scaling limits of systems of jump processes on the integer lattice with local interactions. In particular, this result extends the convergence of TASEP to its continuous analogue. This is joint work with Ioannis Karatzas and Soumik Pal.