A Direct Solution Method for Stochastic Impulse Control Problems of One-dimensional Diffusions

We consider stochastic impulse control problems where the process is driven by a general onedimensional diffusions. Impulse control problems are widely used to financial engineering/decisionmaking problems such as dividend payout problem, portfolio optimization with transaction costs, and inventory control. We shall show a new mathematical characterization of the value function as a linear function in certain transformed space. Our approach can (1) relieve us from the burden of guessing and proving the optimal strategy, (2) present a simple method to find the value function and the corresponding control policies, and (3) handle systematically a broader class of reward and cost functions than the conventional methods of quasi variational inequalities, especially because the existence of the finite value function can be shown in much a simpler way.