A Direct Solution Method for Stochastic Impulse Control Problems of One-dimensional Diffusions

2007/03/07 by Masahiko Egami, Egami, Masahiko
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC

paper · pdf · doi:10.48550/arxiv.math/0703179

arxiv created 2007/03/07 · openalex publication_date 2007/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space. Our approach can relieve us from the burden of guessing and proving the optimal strategy, (2) present a simple method to find the value function and the corresponding control policies, and (3) handle systematically a broader class of reward and cost functions since the existence of the value function can be shown in much a simpler way.

Related

• The Solution to an Impulse Control Problem Motivated by Optimal Harvesting
• Stochastic Impulse Control of Non-Markovian Processes
• The Finite Horizon impulse control Problem with arbitrary cost functions : the Viscosity Solution Approach
• Impulse control of conditional McKean-Vlasov jump diffusions
• Stochastic Variational formulas for solutions to linear diffusion equations