Un enfoque teórico en tiempo continuo para modelos de equilibrio general dinámicos estocásticos

Abstract

This document contains three theoretical contributions that lie in the interplay between stochastic general equilibrium models, dynamic macroeconomics, and optimal control in continuous time. In the first chapter, we study an analytic solution of two continuous-time DSGE models with CRRA preferences, Cobb-Douglas type technology, and shocks in the capital accumulation dynamics that combine a diffusion process with random jumps associated with rare events. The technology factor can take the form of, either a mean-reverting CIR process or a geometric Brownian motion. In the second chapter, we study a stochastic continuous-time one-sector neoclassical growth model of Ramsey type with CRRA utility function and a Cobb-Douglas type technology, with capital accumulation, efectivity and the labor force subject to exogenous shocks that follow diffusion processes with jumps, given by rare events. Finally, in the third chapter, we study a heterogeneous agent problem in continuous time. We analyze the effect of stochastic shocks with jumps in the dynamics and distribution of agent's income, and their impact on consumption, saving and joint distribution of wealth and income. In all models, the dynamic programming principle, the veri cation theorem and the method of finite differences allowed us to find analytical and numerical solutions of the Hamilton-Jacobi-Bellman (HJB) and Kolmogorov-Forward (kF) equations. This allows obtaining the optimal policy functions for the control variables, analyzing in each case analytically and numerically the effects of this type of stochastic shocks on the economic decisions of the agents; as well as highlighting that the use of dynamic models, which follow diffusion processes with jumps, represent economic phenomena in a more realistic way and enrich the analysis in environments with risk and uncertainty.