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In an incomplete continuous-time securities market with uncertainty generatedby Brownian motions, we derive closed-form solutions for the equilibriuminterest rate and market price of risk processes. The economy has a finitenumber of heterogeneous exponential utility investors, who receive partiallyunspanned income and can trade continuously on a finite time-interval in amoney market account and a single risky security. Besides establishing theexistence of an equilibrium, our main result shows that if the investors'unspanned income has stochastic countercyclical volatility, the resultingequilibrium can display both lower interest rates and higher risk premiacompared to the Pareto efficient equilibrium in an otherwise identical completemarket.

Incomplete Continuous-time Securities Markets with Stochastic Income Volatility