Abstract
This paper is concerned with the problem of finding optimal extraction policies for 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 macroeconomic parameters, we model the evolution of the oil price as a mean-reverting regime-switching jump-diffusion process. We formulate this problem as a finite-time horizon optimal control problem, which we solve 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 illustrating these results is presented.
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