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Finance, Economics, and Mathematics by Robert C. Merton, Oldrich A. Vasicek

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Chapter 12General Equilibrium with Heterogeneous Participants and Discrete Consumption Times

Journal of Financial Economics, 108, (2013), pp. 608–614; short version published in FAMe, 2013.

Abstract

The paper investigates the term structure of interest rates imposed by equilibrium in a production economy consisting of participants with heterogeneous preferences. Consumption is restricted to an arbitrary number of discrete times. The paper contains an exact solution to market equilibrium and provides an explicit constructive algorithm for determining the state price density process. The convergence of the algorithm is proven. Interest rates and their behavior are given as a function of economic variables.

Introduction

Interest rates are determined by the equilibrium of supply and demand. Increased demand for credit brings interest rates higher, while an increase in demand for fixed-income investment causes rates to go down. To determine the mechanism by which economic forces and investors' preferences cause changes in supply and demand, it is necessary to develop a general equilibrium model of the economy. Such model provides a means of quantitative analysis of how economic conditions and scenarios affect interest rates.

Vasicek (2005) (Chapter 11 of this volume) investigates an economy in continuous time with production subject to uncertain technological changes described by a state variable. Consumption is assumed to be in continuous time, with each investor maximizing the ...

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