A Mixed Singular/Switching Control Problem for a Dividend Policy with Reversible Technology Investment
| Autor: | Huyên Pham, Stéphane Villeneuve, Vathana Ly Vath |
|---|---|
| Přispěvatelé: | Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Benassù, Serena, Groupe de recherche en économie mathématique et quantitative (GREMAQ), Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de la Recherche Agronomique (INRA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National de la Recherche Agronomique (INRA)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS), Pham, Huyên |
| Jazyk: | angličtina |
| Rok vydání: | 2008 |
| Předmět: |
Statistics and Probability
Mathematical optimization [MATH.MATH-PR] Mathematics [math]/Probability [math.PR] viscosity solutions 60G40 91B70 93E20 Dividend policy mixed singular 01 natural sciences 010104 statistics & probability FOS: Mathematics Optimal stopping 0101 mathematics B- ECONOMIE ET FINANCE 60G40 ComputingMilieux_MISCELLANEOUS Mathematics viscosity solution Stochastic control Mathematical finance Probability (math.PR) 010102 general mathematics 93E20 smooth-fit property Mixed singular/switching control problem Singular control [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 91B70 Variational inequality system of variational inequalities 60G40 91B70 93E20 (Primary) Dividend switching control problem Statistics Probability and Uncertainty Viscosity solution Mathematics - Probability |
| Zdroj: | Annals of Applied Probability Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2008, 18 (3), pp.1164-1200 Annals of Applied Probability, 2008, 18 (3), pp.1164-1200 Ann. Appl. Probab. 18, no. 3 (2008), 1164-1200 |
| ISSN: | 1050-5164 2168-8737 |
| Popis: | We consider a mixed stochastic control problem that arises in Mathematical Finance literature with the study of interactions between dividend policy and investment. This problem combines features of both optimal switching and singular control. We prove that our mixed problem can be decoupled in two pure optimal stopping and singular control problems. Furthermore, we describe the form of the optimal strategy by means of viscosity solution techniques and smooth-fit properties on the corresponding system of variational inequalities. Our results are of a quasi-explicit nature. From a financial viewpoint, we characterize situations where a firm manager decides optimally to postpone dividend distribution in order to invest in a reversible growth opportunity corresponding to a modern technology. In this paper a reversible opportunity means that the firm may disinvest from the modern technology and return back to its old technology by receiving some gain compensation. The results of our analysis take qualitatively different forms depending on the parameters values. Comment: Published in at http://dx.doi.org/10.1214/07-AAP482 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
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