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http://hdl.handle.net/2445/193773
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DC Field | Value | Language |
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dc.contributor.author | Jin, Sixian | - |
dc.contributor.author | Schellhorn, Henry | - |
dc.contributor.author | Vives i Santa Eulàlia, Josep, 1963- | - |
dc.date.accessioned | 2023-02-17T19:06:06Z | - |
dc.date.available | 2023-02-17T19:06:06Z | - |
dc.date.issued | 2020-02 | - |
dc.identifier.issn | 0304-4149 | - |
dc.identifier.uri | http://hdl.handle.net/2445/193773 | - |
dc.description.abstract | In this paper we obtain a Dyson type formula for integrable functionals of a pure jump Lévy process. We represent the conditional expectation of a $\mathscr{F}_T$-measurable random variable $F$ at a time $t \leq T$ as an exponential formula involving Malliavin derivatives evaluated along a frozen path. The series representation of this exponential formula turns out to be useful for different applications, and in particular in quantitative finance, as we show in the following examples: the first one is the pricing of options in the Poisson-Black-Scholes model; the second one is the pricing of discount bonds in the Lévy quadratic model. We also obtain, for the conditional expectation of a function of a finite number of the process values, a backward Taylor expansion, that turns out to be useful for numerical calculations. | - |
dc.format.extent | 21 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Elsevier B.V. | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1016/j.spa.2019.03.019 | - |
dc.relation.ispartof | Stochastic Processes and their Applications, 2020, vol. 130, num. 2, p. 824-844 | - |
dc.relation.uri | https://doi.org/10.1016/j.spa.2019.03.019 | - |
dc.rights | cc-by-nc-nd (c) Elsevier B.V., 2020 | - |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Equacions en derivades parcials | - |
dc.subject.classification | Processos estocàstics | - |
dc.subject.classification | Teoria de jocs | - |
dc.subject.classification | Distribució (Teoria de la probabilitat) | - |
dc.subject.other | Partial differential equations | - |
dc.subject.other | Stochastic processes | - |
dc.subject.other | Game theory | - |
dc.subject.other | Distribution (Probability theory) | - |
dc.title | Dyson type formula for pure jump Lévy processes with some applications to finance | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 698179 | - |
dc.date.updated | 2023-02-17T19:06:06Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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698179.pdf | 359.03 kB | Adobe PDF | View/Open |
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