Optimal loss-carry-forward taxation for the Lévy risk model

► The article considered the optimization problem in the Lévy risk model with tax. ► The article uses stochastic control theory via the Hamilton-Jacobi-Bellman equation. ► The core idea of Theorem 3.1 is cutting off the non-profitable times. ► The optimization problem when γπ may vary in [α,1] is still open.