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September  2007, 8(2): 261-277. doi: 10.3934/dcdsb.2007.8.261

A linear-quadratic control problem with discretionary stopping

Shigeaki Koike 1, , Hiroaki Morimoto 2, and  Shigeru Sakaguchi 2,

1. 

Department of Mathematics, Saitama University, 255 Shimo-Okubo, Urawa, Saitama 338-8570
2. 

Department of Mathematics, Ehime University, Matsuyama, 790-8577, Japan, Japan

Received  September 2005 Revised  March 2007 Published  June 2007

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.
Keywords: Viscosity solution, stopping time, linear-quadratic control..
Mathematics Subject Classification: Primary: 49L25, 60G40; Secondary: 49J4.
Citation: Shigeaki Koike, Hiroaki Morimoto, Shigeru Sakaguchi. A linear-quadratic control problem with discretionary stopping. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 261-277. doi: 10.3934/dcdsb.2007.8.261
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