Starting from an optimal cash management problem and its formulation as a stochastic impulse control problem we will derive an obstacle problem where the obstacle exhibits non-local behavior. The goal of this presentation is to present some regularity results as well as discuss the motivating problem and comment on future work. We start with the 1d model for intuition and then proceed to discuss the higher dimensional analogue. We present two different models for analysis and develop the necessary theory from Elliptic Partial Differential Equations. We also discuss other applications arising from variants of the model particularly in Mathematical Finance and Network Theory.
- http://www.ma.utexas.edu/users/rjain/ - Personal Webpage