Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches

Abstract

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.

25 pages, 3 figures

References in corpus (4)

• On the optimal dividend problem for a spectrally negative Lévy process
• On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes
• Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results
• Optimal investment policy and dividend payment strategy in an insurance company