Due to the COVID-19 Pandemic, the University has instruction to cancel all in-person events through the Spring semester to adhere to city and state orders limiting public gatherings. Events still running must now take place Online— listed events will include a link in which one may access the Online webspace:

To view Mr. Braun’s defense, enter his Online chatroom via Collaborative Ultra— it will open one hour prior to the event at 9:00 am on Friday, June 12th.

A Dynamic Programming Approach to Impulse Control of Brownian Motions

Mr. Robin Braun
University of Wisconsin-Milwaukee
MS Graduate Student – Teaching Assistant

“This thesis considers an impulse control problem of a standard Brownian motion under a discounted criterion, in which every intervention incurs a strictly positive cost. The value function and an optimal $(\tau_{*}, Y_{*})$ policy are found using the dynamic programming principle together with the smooth pasting technique. The thesis also performs a sensitivity analysis by analyzing the limiting behaviors of the value function and the $(\tau_{*}, Y_{*})$ policy when the fixed intervention cost converges to zero. It is demonstrated that the limits agree with the classic fuel follower problem.
The thesis next formulates and analyzes an $N$-player stochastic game of an  impulse control problem under a discounted criterion. In the $N$-player stochastic game, each player controls an object. The objects are molded by an $N$-dimensional Brownian motion.  A key aspect of the formulation is that each player aims to minimize  her total impulse control cost and  the total distance of her object to the moving center of the $N$ objects. The interaction mandates the players to closely follow each other’s movements.  The Nash equilibrium   is characterized and analyzed by a system of Hamilton-Jacobi-Bellman equations. The case when $N=2$ is studied in detail.”

Committee Members:
Profs. David Spade, Richard Stockbridge and Chao Zhu.