On Optimality of Threshold Dividend Strategy for Regime-Switching Diffusions With Negative Exponential Jumps

We consider a dividend optimization problem of de Finetti over an admissible class with restricted dividend rates. The risk process under consideration here evolves as a diffusion with negative exponential jumps modulated by an independent Markov chain. We devote to prove that the regime-switching threshold strategy is the optimal dividend strategy, where the dividend is paid with maximal admissible rate over a threshold level as the function of regime state, while nothing is paid under it. Furthermore, the optimality result holds when an inequality is satisfied