Insurance control for classical risk model with fractional Brownian motion perturbation

In the paper, we consider a classical risk model that is perturbed by a standard fractional Brownian motion with Hurst parameter H∈(12,1). The customers’ input may be considered as a control parameter which allows the firm to reach a desired target at a specified time. By using the completion of squares method, we obtain an expression of the optimal value function and the corresponding optimal control policy.