Connections Between Optimal Stopping and Stochastic Control II: Bounded-Variation Follower Problems

1984 ◽  
Vol 16 (1) ◽  
pp. 16-16 ◽  
Author(s):  
Ioannis Karatzas ◽  
Steven E. Shreve
Keyword(s):  
Brownian Motion ◽  
Control Problem ◽  
Stochastic Control ◽  
Bounded Variation ◽  
Optimal Stopping ◽  
Stochastic Control Problem

The stochastic control problem of tracking a Brownian motion by a process of bounded variation is reduced to a control problem with reflection at the origin, and the latter is related to a question of optimal stopping of Brownian motion absorbed at the origin. Direct probabilistic arguments can be used to show equivalences between the various problems.

Connections between optimal stopping and stochastic control I. Monotone follower problems

1984 ◽  
Vol 16 (1) ◽  
pp. 15-15
Author(s):  
Joannis Karatzas ◽  
Steven E. Shreve
Keyword(s):  
Brownian Motion ◽  
Control Problem ◽  
Stochastic Control ◽  
Optimal Stopping ◽  
Optimal Solutions ◽  
Stochastic Control Problem

The stochastic control problem of tracking a Brownian motion by a non-decreasing process (monotone follower) is related to a question of optimal stopping. Direct probabilistic arguments are employed to show that the two problems are equivalent and that both admit optimal solutions.

A Lower Bounding Linear Programming approach to the Perimeter Patrol Stochastic Control Problem

2012 ◽  
Author(s):  
Krishnamoorthy Kalyanam ◽  
Swaroop Darbha ◽  
Myoungkuk Park ◽  
Meir Pachter ◽  
Phil Chandler ◽  
...  
Keyword(s):  
Linear Programming ◽  
Control Problem ◽  
Stochastic Control ◽  
Programming Approach ◽  
Linear Programming Approach ◽  
Lower Bounding ◽  
Stochastic Control Problem
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