# Optimal Oil Production and Taxation in Presence of Global Disruptions

## TL;DR

This paper develops a mathematical model for optimal oil extraction and taxation considering global market fluctuations, deriving equilibrium policies for producers and governments using stochastic processes and differential game theory.

## Contribution

It introduces a regime-switching jump diffusion model for oil prices and characterizes the Nash equilibrium for extraction and taxation policies.

## Key findings

- Existence of a Nash equilibrium in the model
- Optimal extraction and tax policies derived
- Numerical example illustrating the theoretical results

## Abstract

This paper studies the optimal extraction policy of an oil field as well as the efficient taxation of the revenues generated. Taking into account the fact that the oil price in worldwide commodity markets fluctuates randomly following global and seasonal macroeconomic parameters, we model the evolution of the oil price as a mean reverting regime-switching jump diffusion process. Given that oil producing countries rely on oil sale revenues as well as taxes levied on oil companies for a good portion of the revenue side of their budgets, we formulate this problem as a differential game where the two players are the mining company whose aim is to maximize the revenues generated from its extracting activities and the government agency in charge of regulating and taxing natural resources. We prove the existence of a Nash equilibrium and the convergence of an approximating scheme for the value functions. Furthermore, optimal extraction and fiscal policies that should be applied when the equilibrium is reached are derived.A numerical example is presented to illustrate these results.