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Mathematics and Financial Economics
Erschienen in: Mathematics and Financial Economics 4/2019

28.02.2019

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

verfasst von: Salvatore Federico, Mauro Rosestolato, Elisa Tacconi

Erschienen in: Mathematics and Financial Economics | Ausgabe 4/2019

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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.
Vorheriger Artikel Mean-reverting additive energy forward curves in a Heath–Jarrow–Morton framework
Nächster Artikel Impact of contingent payments on systemic risk in financial networks

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Fußnoten
1
The fact that only positive intervention, i.e. \(i_n>0\), is allowed is expressed in the economic literature of Real Options by saying that the investment is irreversible.
 
2
Other than in [63, Ch. 4, Sec. 5], irreversible and reversible investment problems with no fixed investment costs are largely treated in the mathematical economic literature, both over finite and infinite horizon. We mention, among others [1, 2, 4, 5, 10, 11, 23, 24, 30, 32, 33, 37, 39‐42, 52, 55, 59, 64, 70].
 
3
The stochastic impulse control setting has been widely employed in several other applied fields: e.g., exchange rate [20, 49], portfolio optimization with transaction costs [51, 57], inventory and cash management [27, 67, 68] and real options [47, 53].
 
4
See, e.g. [13, 27, 48, 51, 57] and, in a much more general context of jump-diffusion [60, Ch. 6] for the guess-and-verify approach.
 
5
The smooth-fit principle has also been established, when the diffusion is assumed to be transient, by techniques based on excessive function (see [66]).
 
6
This is a well known rule in the economic literature of inventory problems, see [8, 67, 68].
 
7
Actually, we should consider \(b(x)=\nu x\) if \(x>0\) and \(b(x)=0\) otherwise and similarly for \(\sigma \), in order to fit Assumption 2.1. But this does not matter because our controlled process lies in \(\mathbb {R}_{++}\).
 
8
The simulations are done for negative values of \(\nu \), thinking of it as a depreciation factor. We omit, for the sake of brevity, to report the simulations that we have performed for positive values of \(\nu \), as the outputs show the same qualitative behaviour as in the case of negative \(\nu \).
 
9
In this case the optimal control consists in a reflection policy at a boundary; in other terms the interval [s, S] degenerates in a singleton \(\{s\}=\{S\}\).
 
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Metadaten
Titel
Irreversible investment with fixed adjustment costs: a stochastic impulse control approach
verfasst von
Salvatore Federico
Mauro Rosestolato
Elisa Tacconi
Publikationsdatum
28.02.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Mathematics and Financial Economics / Ausgabe 4/2019
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-019-00238-w

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