Physical Sciences and Mathematics Commons^™

A Dynamic Programming Approach To Impulse Control Of Brownian Motions, Robin Braun

Theses and Dissertations

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 …