Optimal dividend payment strategies with debt constraint in a hybrid regime-switching jump–diffusion model

Senren Tan, Zhuo Jin*, G. Yin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

This paper develops an optimal dividend policy for an insurance company, whose asset and liability have different dynamics, and whose surplus follows a regime-switching jump–diffusion process. The insurer aims to maximize the expected total discounted value of dividends paid out under the debt management constraint. By using the dynamic programming principle, a generalized system of integro-differential Hamilton–Jacobi–Bellman equations is derived. Moreover, this paper studies two cases where the liability of the insurer follows a uniform claim density and a generalized Pareto density in a two-regime economy, respectively. Closed-form solutions of the value functions and the optimal dividend payment strategies are obtained in both cases. A numerical example is provided to illustrate the relationship between the key parameters in the model and the value functions, as well as some interesting economic insights.

Original languageEnglish
Pages (from-to)141-156
Number of pages16
JournalNonlinear Analysis: Hybrid Systems
Volume27
DOIs
Publication statusPublished - Feb 2018
Externally publishedYes

Keywords

  • Debt constraint
  • Dividend strategy
  • Jump–diffusion
  • Regime switching
  • Stochastic control

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