The equilibrium allocation of diffusive and jump risks with heterogeneous agents

Abstract

We study a two-agent pure exchange equilibrium subject to both nondiversifiable diffusive and jump risks. Agents can trade in a financial market consisting of a stock market, a money market, and an insurance market for jump risk. Heterogeneity is introduced through different levels of relative risk aversion. In the framework of standard expected utility we find the surprising result that the less risk averse agent purchases insurance contracts against jump risk from the more risk averse agent. This equilibrium allocation is linked to the non-linear wealth sharing rule in such an economy, and preserves the wealth effects studied by Dumas [Rev. Financ. Stud. 2 (1989) 157] in the case of pure diffusive risk. Since the benchmark economy with homogeneous agents generates no excess uncertainty in the stock market, we study the effect on excess volatility and excess jump size solely due to different levels of relative risk aversion. We observe 3% excess uncertainty in jump sizes for a reasonable specification of economic fundamentals.