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On Skorokhod embeddings and Poisson equations
Döring, Leif
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Gonon, Lukas
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Prömel, David J.
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Reichmann, Oleg
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URL:
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https://arxiv.org/abs/1703.05673
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Weitere URL:
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https://arxiv.org/pdf/1703.05673.pdf
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Dokumenttyp:
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Arbeitspapier
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Erscheinungsjahr:
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2017
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Ort der Veröffentlichung:
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Mannheim [u.a.]
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Sprache der Veröffentlichung:
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Englisch
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Einrichtung:
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Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik > Probability Theory (Döring 2017-)
Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik > Mathematical Finance (Prömel 2019-)
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Fachgebiet:
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510 Mathematik
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Abstract:
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The classical Skorokhod embedding problem for a Brownian motion W asks to find a stopping time τ so that Wτ is distributed according to a prescribed probability distribution μ. Many solutions have been proposed during the past 50 years and applications in different fields emerged. This article deals with a generalized Skorokhod embedding problem (SEP): Let X be a Markov process with initial marginal distribution μ0 and let μ1 be a probability measure. The task is to find a stopping time τ such that Xτ is distributed according to μ1. More precisely, we study the question of deciding if a finite mean solution to the SEP can exist for given μ0,μ1 and the task of giving a solution which is as explicit as possible. If μ0 and μ1 have positive densities h0 and h1 and the generator A of X has a formal adjoint operator A∗, then we propose necessary and sufficient conditions for the existence of an embedding in terms of the Poisson equation A∗H=h1−h0 and give a fairly explicit construction of the stopping time using the solution of the Poisson equation. For the class of Lévy processes we carry out the procedure and extend a result of Bertoin and Le Jan to Lévy processes without local times.
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 | Dieser Eintrag ist Teil der Universitätsbibliographie. |
 Suche Autoren in
BASE:
Döring, Leif
;
Gonon, Lukas
;
Prömel, David J.
;
Reichmann, Oleg
Google Scholar:
Döring, Leif
;
Gonon, Lukas
;
Prömel, David J.
;
Reichmann, Oleg
ORCID:
Döring, Leif  ORCID: https://orcid.org/0000-0002-4569-5083, Gonon, Lukas, Prömel, David J. ORCID: https://orcid.org/0000-0001-7028-7500 and Reichmann, Oleg
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