Optimal Numerical Control of Volterra Integral Equations for a Regulated Risk Model

Under a regulation imposed by a regulatory authority, a general risk model is studied with stationary independent increments. The regulatory authority´s problem is to exercise a regulation barrier and penalties to protect the insured with minimum cost. For an insurance firm with the given regulation, it has to maximize its long run average profit per unit time by seeking an investment-dividend policy. By use of a numerical collocation method of Volterra integral equations, we investigate a joint insurance firm-regulatory authority problem, which is in the concept of Stackelberg strategies in game theory. The resulting values of the optimal control are compared numerically for two types of claim distributions.