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

Abstract

Motivated by recent developments in risk management based on the U.S. bankruptcy code, we revisit the De Finetti’s optimal dividend problem by incorporating the reorganization process and regulator’s intervention documented in Chapter 11 bankruptcy. The resulting surplus process, bearing financial stress towards the more subtle concept of bankruptcy, corresponds to a non-standard spectrally negative Lévy process with endogenous regime switching. Some explicit expressions of the expected 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 Lévy measure is log-convex, the optimal dividend control is shown to be of the barrier type and the associated optimal barrier can be identified using scale functions of spectrally negative Lévy processes. Some financial implications are also discussed in an illustrative example.