Interest Rates and Transaction Costs in Incomplete Equilibria

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

A typical starting point for a financial model takes an asset price as given and manipulates it to determine results. A less studied path asks what makes an asset pricing model good, and where do such good models come from? Equilibrium theory studies the formation of asset pricing models at a fundamental level where an economy's total supply meets its total demand. This award will study two overarching equilibrium projects set in incomplete settings, where not all risk can be captured by trading. The projects use mathematical tools that are now within reach to describe equilibrium-based "good" models involving (i) the formation of interest rates, and (ii) the formation of stock prices in the presence of proportional transaction costs. Both interest rates and transaction costs are highly relevant to financial markets but currently poorly understood in incomplete equilibrium settings. The award will involve collaborations and the involvement and training of graduate students. This award will study two related problems involving equilibrium of stochastic systems in mathematical finance. The first goal is to prove the existence of a finite-agent Radner equilibrium in incomplete market models with stochastic interest rates and proportional transaction costs. After obtaining existence, the investigator will analyze the effects of incompleteness on the endogenously determined asset prices. Mathematically, the analysis draws from systems of fully coupled quadratic backward stochastic differential equations (BSDE), which are doubly reflective in the case of transaction costs. Existence results for such BSDE systems are nonconstructive, which complicates the analysis of incompleteness effects. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.