A linear-quadratic control problem with discretionary stopping

Shigeaki Koike; Hiroaki Morimoto; Shigeru Sakaguchi

doi:10.3934/dcdsb.2007.8.261

Article Contents

2007, Volume 8, Issue 2: 261-277. Doi: 10.3934/dcdsb.2007.8.261

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A linear-quadratic control problem with discretionary stopping

1.
Department of Mathematics, Saitama University, 255 Shimo-Okubo, Urawa, Saitama 338-8570
2.
Department of Mathematics, Ehime University, Matsuyama, 790-8577

Received: August 31, 2005

Revised: February 28, 2007

Published: August 2007

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Abstract

We study the variational inequality for a 1-dimensional linear-quadratic control problem with discretionary stopping. We establish the existence of a unique strong solution via stochastic analysis and the viscosity solution technique. Finally, the optimal policy is shown to exist from the optimality conditions.

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Mathematics Subject Classification: Primary: 49L25, 60G40; Secondary: 49J40.

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