Optimal Oil Production under Mean Reverting L\'evy Models with Regime Switching

TL;DR

This paper models oil prices as a mean reverting regime switching jump diffusion process and derives optimal extraction policies using viscosity solutions, providing a numerical scheme and example.

Contribution

It introduces a novel model for oil prices incorporating regime switching and jumps, and develops a numerical method to find optimal extraction policies.

Findings

Numerical scheme converges to the optimal reward function.

Optimal extraction policies depend on regime states.

Model captures complex price dynamics with practical control solutions.

Abstract

This paper is concerned with the problem of finding the optimal of extraction policies of an oil field in light of various financial and economical restrictions and constraints. Taking into account the fact that the oil price in worldwide commodity markets fluctuates randomly following global and seasonal macro-economic parameters, we model the evolution of the oil price as a mean reverting regime switching jump diffusion process. We formulate this problem as finite-time horizon optimal control problem. We solve the control problem using the method of viscosity solutions. Moreover, we construct and prove the convergence of a numerical scheme for approximating the optimal reward function and the optimal extraction policy. A numerical example that illustrates these results is presented.