We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income . The investors can trade continuously on a finite time interval in a money market account as well as a risky security. Besides establishing the existence of an equilibrium, our main result shows that the resulting equilibrium can display a lower risk-free rate and a higher risk premium relative to the usual Pareto efficient equilibrium in complete markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles .
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously on a finite time-interval in a money market account and a single risky security. Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic countercyclical volatility, the resulting equilibrium can display both lower interest rates and higher risk premia compared to the Pareto efficient equilibrium in an otherwise identical complete market .
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We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors,
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. The investors
and
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time interval
time-interval
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as well as a
and a single
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the
if the investors' unspanned income has stochastic countercyclical volatility, the
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a lower risk-free rate and a higher risk premium relative to the usual
both lower interest rates and higher risk premia compared to the
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complete markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles
an otherwise identical complete market