Mathematics and Financial Economics

, Volume 13, Issue 4, pp 579–616 | Cite as

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

  • Salvatore FedericoEmail author
  • Mauro Rosestolato
  • Elisa Tacconi


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.


Impulse stochastic optimal control Quasi-variational inequality Viscosity solution Irreversible investment Fixed cost 

AMS Subject Classification

93E20 (Optimal stochastic control) 35Q93 (PDEs in connecton woth control and optimization) 35D40 (Viscosity solution) 35B65 (Smoothness and regularity of solutions) 

JEL Classification

C61 (Optimization techniques, programming models, dynamic analysis) D25 (Intertemporal firm choice: investment, capacity and financing) E22 (Investment, capital, intangible capital, capacity) 



The authors are sincerely grateful to the Associate Editor and to two anonymous Referees for their careful reading and very valuable comment that improved the final version of the paper. They also thank Giorgio Ferrari for his very valuable comments and suggestions. Mauro Rosestolato thanks the Department of Political Economics and Statistics of the University of Siena for the kind hospitality in March 2017 and the grant Young Investigator Training Program financed by Associazione di Fondazioni e Casse di Risparmio Spa supporting this visit. He also thanks the ERC 321111 Rofirm for the financial support.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Economia Politica e StatisticaUniversità di SienaSienaItaly
  2. 2.CMAPEcole PolytechniqueParisFrance
  3. 3.Dipartimento di FinanzaBocconi UniversityMilanItaly

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