Morimoto H. Stochastic Control and Mathematical Modeling: Applications in Economics

Cambridge University Press, 2010. — 340 p. — ISBN: 0521195039This is a concise and elementary introduction to stochastic control and mathematical modeling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Contents include the basics of analysis and probability, the theory of stochastic differential equations, variational problems, problems in optimal consumption and in optimal stopping, optimal pollution control, and solving the Hamilton-Jacobi-Bellman (HJB) equation with boundary conditions. Major mathematical prerequisites are contained in the preliminary chapters or in the appendix so that readers can proceed without referring to other materials.Stochastic Calculus and Optimal Control Theory
Foundations of stochastic calculus
Stochastic differential equations: weak formulation
Dynamic programming
Viscosity solutions of Hamilton-Jacobi-Bellman equations
Classical solutions of Hamilton-Jacobi-Bellman equations;
Applications to Mathematical Models in Economics
Production planning and inventory
Optimal consumption/investment models;
8. Optimal exploitation of renewable resources
Optimal consumption models in economic growth
Optimal pollution control with long-run average criteria
Optimal stopping problems
Investment and exit decisions