Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain (Q1627700)

Dividend optimization/risk control problems are of special interest in insurance, where the dividend is a controllable dynamic process. Moreover, the risk of the insurance company is controllable by means of a process called reinsurance. This is an interesting paper focused on the problem of how to running an insurance company to maximize his total discounted expected dividends. In the assumed model, the dividend rate is limited in a closed interval and the company is allowed to reinsure the risk. So there are two strategies which called dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries a following Barenblatt parabolic equation. The authors analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.