On De Finetti’s optimal impulse dividend control problem under Chapter 11 bankruptcy

Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S. bankruptcy code, in this paper we follow [44] to revisit the De Finetti dividend control problem under the reorganization process and the regulator’s intervention documented in U.S. Chapter 11 bankruptcy. We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments. Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem, and hence computations and proofs that are distinct from [44] are needed. To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy, the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching. Some explicit expressions of the expected net present values under a double barrier dividend strategy, new to the literature, are established in terms of scale functions. With the help of these expressions, we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies. When the tail of the Lévy measure is log-convex, this optimal double barrier dividend strategy is then verified as the optimal dividend strategy, solving our optimal impulse control problem.