Essays in financial economics

Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, 2018.Cataloged from PDF version of thesis.Includes bibliographical references.This thesis consists of three chapters on asset pricing, dynamic stochastic general equilibrium and structural estimation of dynamic models. Chapter 1 introduces a global, nonlinear numerical method to solve a large class of continuous-time models in economics and finance. Using modern tools from Machine Learning, I show that the problem of solving the corresponding nonlinear partial differential equations (PDEs) can be recast as a sequence of supervised learning problems. Furthermore, I propose a setting to test and evaluate solution methods. In the context of a Neoclassical Growth Model, given any value function, the productivity function can be reverse engineered so that the Hamilton-Jacobi-Bellman (HJB) equation corresponding to the dynamic optimization problem is identically zero. This provides a testing ground for solution methods. Chapter 2 leverages the algorithm developed in chapter 1 to do structural estimation of stochastic dynamic models in economics. By extending the state space to include all model parameters, I show that we need to solve the model only once to do structural estimation. Parameters are then estimated by minimizing the distance between key empirical moments and the model-implied ones. Unlike the Simulated Method of Moments, the model-implied moments are estimated without the computation of a single moment. Instead, a neural network learns the corresponding moments using raw simulated observations. In chapter 3 I study a multi-sector production-based economy where countercyclical risk premia and capital reallocation lengthens recessions. In the model, risk-aversion increases after negative productivity shocks, and the ensuing capital reallocation propagates the reduction in aggregate productivity and aggregate consumption. The decrease in consumption keeps the risk aversion high, preventing a quick recovery to the balanced growth path.by Victor Duarte.1. Machine Learning for Continuous-Time Economics -- 2, Gradient-Based Structural Estimation -- 3. Sectoral Reallocation and Endogenous Risk-Aversion.Ph. D