Date of Original Version

5-2-2011

Type

Article

Rights Management

This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.jet.2012.01.007

Abstract or Description

In a finite time horizon, incomplete market, continuous-time setting with dividends and investor incomes governed by arithmetic Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and stock price for an economy with a finite set of heterogeneous CARA investors and unspanned income risk. In equilibrium, the Sharpe ratio is the same as in an otherwise identical complete market economy, whereas the riskfree rate is lower and, consequently, the stock price is higher. The reduction in the risk-free rate is highest when the more risk-averse investors face the largest unspanned income risk. In numerical examples with reasonable parameters, the risk-free rate is reduced by several percentage points.

DOI

10.1016/j.jet.2012.01.007

Included in

Mathematics Commons

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Published In

Journal of Economic Theory, 147, 3, 1035-1063.