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research article

Optimal expulsion and optimal confinement of a Brownian particle with a switching cost

Dalang, Robert C.  
•
Vinckenbosch, Laura  
2014
Stochastic Processes And Their Applications

We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a switching cost. In each problem, the value function is written as the solution of a free boundary problem involving second order ordinary differential equations, in which the unknown boundaries are found by applying the principle of smooth fit. For both problems, we compute the value function, we exhibit the optimal strategy and we prove its generic uniqueness. (C) 2014 Elsevier B.V. All rights reserved.

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Type
research article
DOI
10.1016/j.spa.2014.07.016
Web of Science ID

WOS:000343355200008

Author(s)
Dalang, Robert C.  
Vinckenbosch, Laura  
Date Issued

2014

Publisher

Elsevier Science Bv

Published in
Stochastic Processes And Their Applications
Volume

124

Issue

12

Start page

4050

End page

4079

Subjects

Stochastic control with switching cost

•

Principle of smooth fit

•

Free boundary problems

•

Martingale method

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
PROB  
Available on Infoscience
December 30, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/109655
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