In this paper we want to optimize premium and reserve in an optimal control insurance model. A simple parameterisation that represents the insurance market’s response to an insurer adopting a pricing strategy determined via optimal control theory is introduced. The criterion is that of minimizing exponential utility. A special feature of our construction is to allow for convergence of the reserves to expected reserve at the end of the planning period. We control the premium in order to minimize the loss ratio and reach to the expected reserve. If the market reacts, then the optimal strategy also changes and the premium may take an increasing (decreasing) shift that will result in more (less) insurance sales. After explaining the model, using numerical examples, one of the parameters is estimated using the statistic science followed by solving the problem using PMP method.
