Risk aversion heterogeneity and the investment-uncertainty relationship: a closed-form formulation

A simple dynamic general-equilibrium model of savings and investment is populated by agents with Kreps-Porteus preferences. Households are heterogeneous in their risk aversion, which explains the negative relationship between aggregate investment and aggregate volatility. Agents trade riskless assets to share the aggregate risk, so that in equilibrium a higher volatility increases the certainty-equivalent future return for low-risk-averse individuals, which hold a long position in risky assets. The certainty-equivalent return may also increase for high-risk-averse agents, who hold safe assets. In response to this rise, savings and investment decrease due to a limited willingness to substitute consumption over time