Optimal advertising strategies in a sports licensing contract

We consider a licensing agreement that grants to a manufacturer (licensee) the rights to use the logo of a sports team (licensor) on the goods he produces. This contract stands over a royalty clause that re- quires that the licensee pays a financial reward to the licensor. A further payment can sometimes be required in terms of a sales percentage, in case the sales exceed a given amount. We take into account this partic- ular clause by considering a non-differentiable scrap value term in the objective functional of the licensee. We formulate and solve an optimal control problem, with non differentiable dependence on final state, in order to find the optimum advertising strategies for the licensee.