Publication
Dynamic programming for a Markov-switching jump–diffusion
| dc.contributor.author | Azevedo, N. | |
| dc.contributor.author | Pinheiro, D. | |
| dc.contributor.author | Weber, G.-W. | |
| dc.date.accessioned | 2015-01-09T10:08:46Z | |
| dc.date.available | 2015-01-09T10:08:46Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities. | por |
| dc.description.sponsorship | We thank an anonymous referee for several comments and suggestions that helped improve the final version of this paper. N. Azevedo’s research was supported by FCT—Fundação para a Ciência e a Tecnologia grant with reference SFRH-BD67186-2009. N. Azevedo also thanks the financial support of CEMAPRE and FCT—Fundação para a Ciência e a Tecnologia through the Program POCI 2010. | |
| dc.identifier.citation | In "Journal of Computational and Applied Mathematics". ISSN 0377-0427. 267 (2014) 1-19 | por |
| dc.identifier.doi | 10.1016/j.cam.2014.01.021 | |
| dc.identifier.issn | 0377-0427 | |
| dc.identifier.uri | http://hdl.handle.net/10400.22/5367 | |
| dc.language.iso | eng | por |
| dc.peerreviewed | yes | por |
| dc.publisher | Elsevier | por |
| dc.relation | SFRH-BD67186-2009 | |
| dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0377042714000491 | por |
| dc.subject | Stochastic optimal control | por |
| dc.subject | Jump–diffusion | por |
| dc.subject | Markov-switching | por |
| dc.subject | Optimal consumption–investment | por |
| dc.title | Dynamic programming for a Markov-switching jump–diffusion | por |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 19 | por |
| oaire.citation.startPage | 1 | por |
| oaire.citation.title | Journal of Computational and Applied Mathematics | por |
| oaire.citation.volume | 267 | por |
| person.familyName | Azevedo | |
| person.givenName | Nuno | |
| person.identifier.ciencia-id | 6A15-4983-3890 | |
| person.identifier.orcid | 0000-0002-7287-3535 | |
| person.identifier.rid | E-6194-2014 | |
| rcaap.rights | openAccess | por |
| rcaap.type | article | por |
| relation.isAuthorOfPublication | d781eb4f-8595-465e-8910-3ee8dbc2d67b | |
| relation.isAuthorOfPublication.latestForDiscovery | d781eb4f-8595-465e-8910-3ee8dbc2d67b |