Explicit Solutions for Optimal Resource Extraction Problems under Regime Switching L\'evy Models

TL;DR

This paper derives explicit solutions for optimal resource extraction strategies considering market prices modeled by Markov switching Le9vy processes, accounting for macroeconomic fluctuations and providing practical extraction policies.

Contribution

It introduces closed-form solutions for the value function and optimal extraction policy under complex stochastic price models with regime switching and jumps.

Findings

Closed-form solutions for value function and policies

Numerical examples demonstrating effectiveness

Model captures macroeconomic fluctuations in prices

Abstract

This paper studies the problem of optimally extracting nonrenewable natural resources. Taking into account the fact that the market values of the main natural resources i.e. oil, natural gas, copper,..., etc, fluctuate randomly following global and seasonal macroeconomic parameters, the prices of natural resources are modeled using Markov switching L\'evy processes. We formulate this optimal extraction problem as an infinite-time horizon optimal control problem. We derive closed-form solutions for the value function as well as the optimal extraction policy. Numerical examples are presented to illustrate these results.