Solvability of a class of absorption problems with optimal operational scale and withdrawal control

This paper addresses a class of value-maximization problems in storage-type optimal control involving operational scale and withdrawals with absorption. Moving beyond the drifted Brownian motion model, we develop a unified methodological approach under a general linear diffusion framework. We demonstrate the solvability of a broad class of problems by deriving semi-explicit optimal strategies. We further establish conditions for the existence of fully explicit solutions and illustrate solution methods with examples based on models for a variety of scenarios, both where explicit solutions exist and where only semi-explicit solutions are available.