Irreversible investment with fixed adjustment costs: a stochastic impulse control approach

2018/01/13 by Federico, Salvatore, Rosestolato, Mauro, Tacconi, Elisa
#35B65 #35D40 #35Q93 #93E20 #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1801.04491

Abstract

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to the associated quasi-variational inequality. This enables us to characterize the structure of the continuation and action regions and construct an optimal control. Finally, we focus on the linear case, discussing, by a numerical analysis, the sensitivity of the solution with respect to the relevant parameters of the problem.

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