The Department of Finance and Risk Engineering welcomes Kim Weston, Assistant Professor of Mathematics, Rutgers University to the BQE Lecture Series.
Equilibrium Existence in a Limited Participation Economy
A limited participation economy models the real-world phenomenon that some investors have access to more of the market than others. Basak and Cuoco (RFS'98) introduced a continuous-time, running consumption model of limited participation with two (classes of) investors: an unconstrained investor with access to a complete market, and a constrained investor who cannot trade in the stock market and faces incompleteness. Equilibrium existence results have so far been limited to considering logarithmic constrained investors, in part due to the complications that arise with an endogenously-determined stochastic interest rate. In this talk, I will discuss an extension of Basak and Cuoco's model to the case of exponential investors. Equilibrium is described by a coupled system of two quadratic BSDEs, whose form relies on the presence of a traded annuity that is accessible to both the constrained and unconstrained investors. My equilibrium existence proof is based on proving existence for a coupled BSDE system with a triangular-quadratic structure of its drivers.
Kim Weston is an assistant professor of mathematics at Rutgers University. She completed her Ph.D. in 2016 with Dmitry Kramkov at Carnegie Mellon University and served as an NSF postdoctoral fellow at the University of Texas at Austin and Rutgers in 2016-2018. Kim is interested in stochastic control and stochastic analysis questions that arise from financial economics. Her current interests include studying systems of equations related to financial equilibrium, especially in the presence of frictions.