Extensions of finite-horizon reversible investment dynamics and interactions

Investigate finite-horizon reversible investment problems with state-dependent adjustment costs, more general economic-factor dynamics including mean-reverting and jump-diffusion processes, and equilibrium interactions among firms.

Background

The paper analyzes reversible investment with constant proportional purchase and salvage costs, an exogenous multi-dimensional geometric Brownian motion, and a single risk-neutral firm. Its analytical results rely on these specifications to reduce the problem to a parabolic double-obstacle problem and to construct an optimal reflected capacity process.

The conclusion explicitly identifies relaxing the adjustment-cost structure, the factor dynamics, and the single-firm setting as unresolved extensions. These directions would test whether the singular-control/optimal-switching correspondence, free-boundary characterization, and verification argument remain valid in substantially richer economic environments.