Optimal dividend payout under stochastic discounting

Adopting a probabilistic approach we determine the optimal dividend payout policy of firm whose surplus process follows controlled arithmetic Brownian motion and cash-flows are discounted at stochastic dynamic rate. Dividends can be paid to shareholders unrestricted rates so that problem is cast as one singular control. The interest rate modeled by Cox–Ingersoll–Ross (CIR) firm's objective maximize total expected flow dividends until possible insolvency time. We find an which such kept below endogenously determined threshold expressed decreasing continuous function current value. also prove value control solves variational inequality associated second-order, non-degenerate elliptic operator, with gradient constraint.