Abstract The main continuous time Leech problems considered in this paper are based on stable rational finite dimensional operator-valued functions G and K . Here means that do not have poles the closed right half plane including infinity, problem is to find a operator solution X such $$\begin{aligned} G(s)X(s) = K(s) \quad (s\in \mathbb {C}_+) \hbox {and}\quad \sup \{ \Vert X(s) :\Re s \ge 0 \...

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 ...