Chapter 1 develops a continuous-time, heterogeneous agents version of the Barro-Rietz rare disasters model. Following Gabaix (2012), the disaster probability is assumed to be time-varying. The economy consists of two types of agents: (1) a "rational" agent, who updates his beliefs using Bayes Rule, and (2) a "robust" agent, who updates his beliefs using a pessimistically distorted prior. Following Hansen and Sargent (2008), pessimism is disciplined using detection error probabilities. Disaster risk is assumed to be nontradeable. The model is calibrated to US data, and focuses on three disaster episodes: (1) The Great Depression of 1929-33, (2) The Financial Crisis of 2008-09, and (3) The Covid Pandemic of 2020. The key contribution of the paper is to show that the model can replicate the observed spike in trading volume that occurs during disasters. Trading produces endogenous low frequency dynamics in the distribution of wealth. The relative wealth of robust agents gradually declines during normal times, but rises sharply during disasters. These results sound a note of caution when interpreting short-run movements in the distribution of wealth. Chapter 2 examines the market selection hypothesis in a continuous time asset pricing model with jumps. It is shown that the hypothesis is valid when agents have log preferences. The result is robust as it does not depend on whether markets are incomplete. Jumps affect long-run wealth dynamics through a redistribution channel: Disasters lead to large wealth redistribution as agents with heterogeneous beliefs about disasters have different exposures to risky assets. Using tools from ergodic theory, I prove a novel result that generalizes the rationality concept in the existing literature: an agent endowed with the optimal filter will outperform other agents in complete financial markets asymptotically. Chapter 3, a joint paper with Xiaowen Lei, develops a continuous-time overlapping generations model with rare disasters and agents who learn from their own experiences. Using microdata about household finance in China, we establish that economic disasters such as the Great Leap Forward make investors distrustful of the market. Generations that experience disasters invest a lower fraction of their wealth in risky assets, even if similar disasters are not likely to occur again during their lifetimes. "Fearing to attempt" therefore inhibits wealth accumulation by these "depression babies" relative to other generations.
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