Discounted optimal stopping problems in continuous hidden Markov models

We study a two-dimensional discounted optimal stopping problem related to the pricing of perpetual commodity equities in model financial markets which behaviour underlying asset price follows generalized geometric Brownian motion and dynamics convenience yield are described by an unobservable continuous-time Markov chain with two states. It is shown that time exercise first at spot paid return fixed coupon rate hits lower stochastic boundary being monotone function running value filtering estimate state chain. rigorously prove regular for region relative resulting diffusion process continuously differentiable respect both variables. verified means change-of-variable formula local on surfaces determined as unique solution associated parabolic-type free-boundary problem. also give closed-form case observable