Modeling oil production and its peak by means of a stochastic diffusion process based on the Hubbert curve

The estimation of peak time (and consequently peak value) is approached from two perspectives: one, by obtaining the maximum likelihood point estimation of the two values (both of them can be expressed as parametric functions); the other, by formulating the peak-time as a first-passage-time problem. Finally, in order to validate the methodology developed, we carry out some studies based on simulated data, and then we consider some real-world applications to crude oil production data for Norway and Kazakhstan.