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Quadrature of discontinuous SDE functionals using Malliavin integration by parts
Altmayer, Martin
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Dokumenttyp:
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Buch
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Erscheinungsjahr:
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2015
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Ort der Veröffentlichung:
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München
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Verlag:
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Verlag Dr. Hut
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ISBN:
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978-3-8439-2238-8
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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 > Wirtschaftsmathematik II: Stochastische Numerik (Neuenkirch 2013-)
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Fachgebiet:
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510 Mathematik
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Normierte Schlagwörter (SWD):
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Numerische Mathematik , Malliavin-Kalkül , Stochastische Differentialgleichung
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Freie Schlagwörter (Englisch):
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Heston model , SDE , Malliavin calculus
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Abstract:
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One of the major problems in mathematical finance is the pricing of options. This requires the computation of expectations of the form E(f(S_T)) with S_T being the solution to a stochastic differential equation at a specific time T and f being the payoff function of the option. A very popular choice for S is the Heston model.
While in the one-dimensional case E(f(S_T)) can often be computed using methods based on PDEs or the FFT, multidimensional models typically require the use of Monte-Carlo methods. Here, the multilevel Monte-Carlo algorithm provides considerably better performance - a benefit that is however reduced if the function f is discontinuous. This thesis introduces an approach based on the integration by parts formula from Malliavin calculus to overcome this problem: The original function is replaced by a function containing its antiderivative and by a Malliavin weight term. We will prove that because the new functional is continuous, we can now apply multilevel Monte-Carlo to compute the value of the original expectation without performance reduction.
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Zusätzliche Informationen:
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Zugl.: Mannheim, Univ., Diss., 2015
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 | Dieser Eintrag ist Teil der Universitätsbibliographie. |
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