Optimal dividend strategy for an insurance group with contagious default risk

Abstract

This paper studies the optimal dividend for a multi-line insurance group, in which each subsidiary runs a product line and is exposed to some external credit risk. The default contagion is considered such that one default event may increase the default probabilities of all surviving subsidiaries. The total dividend problem for the insurance group is investigated and we find that the optimal dividend strategy is still of the barrier type. Furthermore, we show that the optimal barrier of each subsidiary is modulated by the default state. That is, how many and which subsidiaries have defaulted will determine the dividend threshold of each surviving subsidiary. These conclusions are based on the analysis of the associated recursive system of Hamilton-Jacobi-Bellman variational inequalities (HJBVIs). The existence of the classical solution is established and the verification theorem is proved. In the case of two subsidiaries,

Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence

“…For example, one may consider the objective functional similar to Bo et al (2021) to minimize the discounted accumulative monetary supply of the central bank subjecting to the dynamic floor constraints that the log-monetary reserve in each bank needs to stay above a prescribed capital level at all times. Beyond the interbank application, one may also modify the singular control problem in Jin et al (2021) as a centralized optimal dividend control by a sizable insurance group in models with N and infinitely many subsidiaries when subsidiaries interact with others by default contagion and some fixed reinsurance rate.…”

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

“…For some comprehensive surveys on developments in optimal dividends and related methodology, we refer to Albrecher and Thonhauser (2009), Avanzi (2009) and references therein. Recently, more interesting new variations on optimal dividend have emerged by considering different risk factors, control constraints and model generalizations, such as Cheung and Wong (2017), Pérez et al (2018), Avanzi et al (2020), Cheng et al (2020), De Angelis (2020), Noba et al (2020), Zhu et al (2020), Jin et al (2021), Avanzi et al (2021), Noba (2021), just to name a few.…”

Mean Field Game of Optimal Relative Investment with Jump Risk

“…See, for example, Bo and Capponi (2018), Bo et al (2019a), Bo et al (2019b), Shen and Zou (2020), Bo et al (2021) among others that are based on the interacting intensity framework, allowing the credit default in one risky asset to increase the default intensities of other surviving names. See also Jin et al (2021) in the context of optimal dividend control for an insurance group.…”