On optimality of barrier dividend control under endogenous regime switching with application to Chapter 11 bankruptcy

Motivated by recent developments in risk management based on the U.S. bankruptcy code, we revisit De Finetti optimal dividend problems by incorporating the reorganization process and regulators intervention documented in Chapter 11 bankruptcy. The resulting surplus process, bearing financial stress towards the more subtle concept of bankruptcy, corresponds to non-standard spectrally negative Levy processes with endogenous regime switching. In both models without and with fixed transaction costs, some explicit expressions of the expected net present values under a barrier strategy, new to the literature, are established in terms of scale functions. With the help of these expressions, when the tail of the Levy measure is log-convex, the optimal dividend control in each problem is verified to be of the barrier type and the associated optimal barrier can be obtained in analytical form.