Finite-Horizon Reversible Investment under Multi-Factor Dynamics

Abstract: We study a finite-horizon reversible investment problem in which a risk-neutral firm adjusts capacity at a proportional purchase cost and a lower salvage value under multi-factor geometric Brownian motion. Via the singular control--optimal switching correspondence, the marginal value of capacity solves a family of parabolic double-obstacle problems. We prove existence, uniqueness and local Sobolev regularity of the strong solution, characterize investment, waiting and disinvestment regions by continuous, strictly separated free boundaries, and verify optimality of the reflected capacity process. Numerically, joint demand improvements shift both boundaries super-additively, 1.5--2.7 times as strongly at the disinvestment boundary, depending on factor correlation.