Impulse Control of Standard Brownian Motion: Discounted Criterion

Abstract : This paper examines the impulse control of a standard Brownian motion under a discounted criterion. In contrast with the dynamic programming approach, this paper first imbeds the stochastic control problem into an infinite-dimensional linear program over a space of measures and derives a simpler nonlinear optimization problem that has a familiar interpretation. Optimal solutions are obtained for initial positions in a restricted range. Duality theory in linear programming is then used to establish optimality for arbitrary initial positions.
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Kurt Helmes, Richard Stockbridge, Chao Zhu. Impulse Control of Standard Brownian Motion: Discounted Criterion. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. pp.158-169, ⟨10.1007/978-3-662-45504-3_15⟩. ⟨hal-01286408⟩

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