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

TL;DR

This paper extends the classical dividend optimization problem to a complex setting involving endogenous regime switching and bankruptcy reorganization, deriving explicit barrier strategies and their optimality conditions.

Contribution

It introduces a novel model with endogenous regime switching for surplus processes and derives explicit barrier strategies using scale functions, advancing the theoretical understanding of optimal dividends under bankruptcy.

Findings

Optimal barrier dividend strategy is identified when Levy measure tail is log-convex.

Explicit expressions for expected present values are derived using scale functions.

The model provides insights into financial decision-making during bankruptcy reorganization.

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 Levy 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 Levy 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 Levy processes. Some financial implications are also discussed in an illustrative example.