Optimal Dividends for a Two-Dimensional Risk Model with Simultaneous Ruin of Both Branches

Research output: Contribution to journalResearch articleContributedpeer-review



We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions.


Original languageEnglish
Article number116
Issue number6
Publication statusPublished - 2 Jun 2022

External IDs

Scopus 85131738889
WOS 000816370500001
Mendeley 6be5b053-10ee-3ce4-9a42-aa0ea384a123



  • Hamilton-Jacobi-Bellman equation, admissibility, compound Poisson process, degenerate risk model, dividends, dynamic programming principle, optimal strategy, simultaneous ruin, stochastic control, viscosity solution

Library keywords