Risk Assessment and Decision Making Under Uncertainty with Applications

Columbia University, New York NY

Investigators

Abstract

This project studies stochastic models applied in social sciences as well as their mathematical foundations. The first part concerns the economics of climate change. Climate change could be a very impactful global risk; its mitigation becomes an interdisciplinary challenge involving a multitude of sciences and agencies. The second part studies how collective behavior can result from individual preferences in stochastic games; this is useful to understand macroscopic effects in systems with many decision-takers, such as financial crises in securities markets. The third part investigates the emergence of speculative price bubbles in asset markets as a consequence of heterogeneity among market participants. The fourth part studies the existence of probability densities for certain stochastic processes and produces estimates for these densities. The complexity of the climate response and its interaction with the economy gives rise to model ambiguity and stochastic uncertainty in decision making. Nevertheless, the existing literature largely relies on deterministic models. This project aims to emphasize the impact of uncertainty and ambiguity on risk assessment and policy making, as well as initiating a transfer of knowledge from fields such as mathematical finance where stochastic models are routinely employed. Regarding stochastic games, the project studies models with mean field interaction which, at least formally, correspond to games with a continuum of players. It is expected that multiplicity of equilibria is related to coalitions of agents, and a notion of stability may be useful to understand why certain equilibria of mean field games are limits of N-player games but others are not. The third project will continue recent work that aims to develop a robust stochastic model for speculation among heterogeneous agents and investigate how market regulations and the distribution of beliefs among market participants influence prices and speculative trading in a bubble. The study of probability densities for stochastic processes follows a novel approach based on optimal control theory. It allows for remarkably general processes, including non-Markovian ones, while being elementary in nature. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.