Impulse Control of Standard Brownian Motion: Discounted Criterion
Résumé
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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