Finite Horizon Optimal Dividend and Reinsurance Problem Driven by a Jump-Diffusion Process with Controlled Jumps

Optimal dividend payout problem under both diffusion risk and Poisson risk in finite horizon

“…x, from which it can be obtained that the right side of the free boundary is the dividend payout region and the left side is the non-dividend payout region. This is also the key that one can transform the singular control problem on v into an equivalence obstacle problem on its gradient u = v x , see e.g., [2,17,15,14]. However, because the integral term in the equation in our problem is nonlocal, the equation on v xx or its approximation analog to those in [17,15,14] cannot be obtained, which prevents us from deriving the concavity of the solution w.r.t.…”