A Singular Control Problem with Discretionary Stopping for Geometric Brownian Motions

Authors:
Hiroaki Morimoto
Affiliations:
morimoto@mserv.sci.ehime-u.ac.jp
Venue:
SIAM Journal on Control and Optimization
Year:
2010

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Abstract

In this paper, we discuss a combined singular control problem with discretionary stopping for geometric Brownian motions. By the method of penalization, we solve the degenerate variational inequality associated with this problem. Its solution $v$ coincides with the value function and, by the concavity of $v$, an optimal control is shown to exist.