Mathematical Finance, Stochastic Analysis, and Machine Learning By Kim Weston: Equilibrium Existence in a Limited Participation Economy

Speaker:

Kim Weston, Rutgers University

Title:

Equilibrium Existence in a Limited Participation Economy

Abstract:

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.

 

Mathematical Finance, Stochastic Analysis, and Machine Learning