Live fast, die young : equilibrium and survival in large economies

We model a continuous-time economy with a continuum of investors who differ both in belief and time preference rate and analyze the impact of these heterogeneities on the behavior of financial markets. In particular, we allow the two types of heterogeneity to be correlated: a negative correlation means that the most optimistic agents are also the most patient ones. We fully characterize the risk-free rate which is procyclical and the market price of risk which is countercyclical. When the two types of heterogeneity are negatively correlated, the former is higher and the latter lower compared to the standard case. A negative correlation also leads to a higher market volatility. Moreover, we find that the trading volume increases with the variance of the belief heterogeneity distribution. Finally, the surviving agent of this economy is not necessarily the one who maximizes her utility over her lifetime: a shorter life might be more rewarding than a longer one.