ADVANCED MATHEMATIC METHODS ENVIRONMENT & RESOURCE ECONOMICS

The most interesting issues in environmental and resource economics have an explicit temporal dimension, since variables of interest such as pollutants, greenhouse gases, biomass of biological resources, or the stocks of fossil fuels accumulate in the ambient environment or are depleted through human actions and natural processes.

The purpose of these lectures is to present the mathematical tools for analyzing environmental and resource management issues in a dynamic set-up.

The lectures include a brief description of differential equations and then move on to describe methods of optimal control, dynamic programing, and differential games. The final chapters cover two novel topics: (1) environmental issues characterized by deep uncertainty, and aversion to ambiguity using robust control methods and formulations of precautionary policies; and (2) the study of pollution/resource management in space and time when the environmental variables evolve in time and diffuse in space.

The lectures are a valuable tool for advanced graduate students in environmental and resource economics who are studying dynamic problems.

Contents:

• Preface
• About the Author
• Differential Equations
• Stability
• Optimal Control and the Principle of Optimality
• Calculus of Variations
• Optimal Control
• Optimal Control: Steady State Analysis
• Linear Optimal Control and Bang-Bang Solutions, Most Rapid Approach Paths
• Constrained Optimal Control
• Dynamic Programming, Continuous Time
• Dynamic Optimization, Discrete Time
• Stochastic Control: Stochastic Processes and Stochastic Calculus
• Optimal Stochastic Control
• Differential Games
• Nonlinear Differential Games in Environmental and Resource Economics: International Pollution Control (The Lake Problem)
• Robust Control
• Optimal Control under Spatio-temporal Dynamics: Optimal Control in Infinite Dimensional Spaces
• Selected Bibliography
• Index

Readership: Graduate students specializing in environmental and resource economics and studying dynamic problems.