Insurance rating to increase the capital of the insurer using the theory of optimal control

Determining the appropriate insurance premium for wealth insurance companies is important to increase revenue. In this paper, we want to optimize premium in order to increase the wealth insurance companies via optimal control theory based on choosing the appropriate risk. Determining appropriate premium, depending on the average market premium and such amount of losses, can lead to increase in the wealth of the insurance company. First, a dynamic model is expressed to describe the receipt of premium and the payment of losses. Then we introduce the premium variable as the problem control variable. In the next step, we define an appropriate objective function for the control variable and state variables in order to increase wealth and the proportionality of the premium to the average market premiume. Then, one of the principal variables is estimated by statistical methods and solves the control problem via the Pontryagin method. Finally, two numerical examples are presented.