Equilibrium Singular Dividend Control with Regime Switching and Bankruptcy under Non-Exponential Discounting

Abstract

This paper studies an infinite-horizon equilibrium dividend problem for a firm whose surplus follows a diffusion with observable Markov regime switching and is absorbed at bankruptcy. Dividend payments are modeled as singular controls, and non-exponential discounting gives rise to time inconsistency. We formulate equilibrium control laws and establish a verification theorem for a general finite-state model with surplus-dependent coefficients. For a two-state model with constant positive drifts and volatilities and bi-exponential discounting, we prove the existence of a regime-dependent equilibrium barrier strategy for arbitrary positive switching intensities. The proof relies on uniform estimates for a system of coupled boundary-value problems and the Poincaré-Miranda theorem. We also verify that the resulting strategy satisfies the equilibrium variational inequalities. Numerical results show that greater dispersion in discount rates, with the initial average discount rate held fixed, raises both barriers. The effect of switching intensity can be nonmonotone and may reverse the ordering of the barriers.