Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes

Abstract The optimal dividends problem has remained an active research field for decades. For insurance company with reserve modelled by a spectrally negative Lévy process having finite first-order moment, we study the impulse dividend and capital injection (IDCI) strategy maximizing expected accumulated discounted net payment subtracted cost of injecting capital. In this setting, beneficiary injects to ensure non-negative risk so that insurer never goes bankrupt. IDCI together its value function is obtained. Besides, two numerical examples are provided illustrate features strategies. impacts model parameters also studied.