### Mathematics Colloquium

** Jin Ma
**

University of Southern California

**Title:** On Kyle-Back Equilibrium Problem-The Case of Dynamic Information

**Date:** Friday, October 29, 2021

**Place and Time:** Zoom, 3:05-3:55 pm

**Abstract.**

We consider the well-known Kyle-Back Strategic Insider Trading problem in the case of dynamic information. Specifically, we assume that, besides knowing the law of the underlying asset at a future time, the insider also observes the liquidity value of the asset dynamically. Assuming that the market price is determined via a Bertrand competition, hence the optional projection of the underlying asset value, we Markovize it by introducing an auxiliary diffusion process in the spirit of the weighted total order process, through a set of 'pricing rule' functions. By considering a class of stochastic Two-Point Boundary Value (TPBV) problems, which removes one of the requirements of the popular dynamic Markov bridge in the literature, we propose a solution scheme for the equilibrium problem under a very general model of the underlying asset. In the case when the solution of TPBV has an affine structure, we show that the pricing rule functions, whence the KyleBack equilibrium, can be determined by the decoupling field of a forwardbackward SDE obtained via a non-linear filtering approach. This talk is based on the joint work with Ying Tan.