We propose an equilibrium model of exhaustible resources in a comprehensive setting, including exploration, stochastic demand, and stochastic reserve, by extending the models in Pindyck (1980) and Anderson, Kellogg, and Salant (2018). The production adjustments can be quite general, e.g., sudden...

In this paper, we derive a parabolic variational inequality with double time-like variables from a continuous exercise model of American call options proposed in Rogers and Schienkman (2007). Using viscosity approach, we prove that the value function is a unique viscosity solution to the...