Optimal dividend strategy for an insurance group with contagious default risk

Zhuo Jin, Huafu Liao, Yue Yang, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

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, the value function and optimal barriers are given in analytical forms, allowing us to conclude that the optimal barrier of one subsidiary decreases if the other subsidiary defaults.

Original languageEnglish
Pages (from-to)335-361
Number of pages27
JournalScandinavian Actuarial Journal
Volume2021
Issue number4
DOIs
Publication statusPublished - May 2021

Keywords

  • credit default contagion
  • default-state-modulated barriers
  • Insurance group
  • optimal dividend
  • recursive system of HJBVIs

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this