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 one-dimensional diffusions. Impulse control problems are widely applied to financial engineering and decision-making problems including dividend payout problem, portfolio optimization with transaction costs, and inventory control. We shall show a new mathematical characterization of the value function in the continuation region as a linear function in certain transformed space. The merits of our approach are as follows: (1) one does not have to guess optimal strategies or verify the optimality via a verification lemma, (2) the method of finding the solution (based on the new characterization of the value function) is simple and direct and thereby (3) one can handle a broader class of reward and cost functions than the conventional methods that use quasi-variational inequalities. Key Words: Stochastic impulse control, Diffusions, Optimal stopping, Concavity. AMS Subject Classification: Primary: 49N25 Seconda...

• Type: Journal
• Year: 2008
• Where: SIAMCO
• Authors: Masahiko Egami
• Keywords: Impulse Control Problems, SIAMCO 2008, Stochastic Impulse Control, Value Function