Rare event risk in a capital market equilibrium

My dissertation examines the question how rare event risk, in addition to small diffusive risk, is optimally shared among market participants in a capital market. In particular, within an equilibrium model I study how two natural sources of heterogeneity affect prices and allocations, heterogeneity in risk aversion and heterogeneity in beliefs. A rare event is assumed to be a jump in economic fundamentals, and a systematic source of uncertainty.; In the second chapter, I focus on heterogeneity in risk aversion. I study a two-agent exchange economy, where agents can trade in a financial market consisting of a stock market, a money market, and an insurance market for rare event risk. In the framework of standard expected utility I 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. Since the benchmark economy with homogenous agents generates no excess uncertainty in the stock market, I study the effect on excess volatility and excess jump size solely due to different levels of relative risk aversion. I observe 3% excess uncertainty in jump sizes for a reasonable specification of economic fundamentals. In the third chapter, I focus on heterogeneity in beliefs about the frequency of rare events. Suppose the rare event is a negative jump leading to a market crash. The agent who anticipates less frequent jumps is willing to provide insurance against rare events for the agent anticipating a higher frequency. In the incomplete market where insurance is absent, the agent who anticipates less frequent jumps is optimally leveraging the portfolio. In this case, I find the surprising result that the equity premium of the stock market decreases. Under the assumption of logarithmic preferences, this is equivalent to an increasing interest rate. The result is linked to the non-linear risk sharing rule for rare event risk in the case of heterogeneity. Portfolio and price adjustments at the occurrence of a rare event can be very large. The model can be extended to capture the friction of heterogeneity in beliefs about the jump size, while agreeing on the frequency of rare events. I show a calibration of the model to catastrophe bonds linked to earthquake risk.; The modeling part of my dissertation is based on three major concepts. First, I utilize a continuous-time pure exchange economy. The (exogenous) aggregate dividend process is assumed to follow a jump-diffusion process. Second, equilibria are characterized using martingale techniques. Third, I use a representative agent construction with stochastic weights to capture the effect of heterogeneous beliefs and possible incompleteness.