Analysis of the Discontinuous Galerkin Method Applied to the
European Option Pricing Problem

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Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem

Přehled o publikaci

D 2013

Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem

HOZMAN, Jiří

Základní údaje

Originální název

Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem

Autoři

HOZMAN, Jiří (203 Česká republika, garant, domácí)

Vydání

Melville, NY, USA, 39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE13), AIP Conference Proceedings 1570, od s. 227-234, 8 s. 2013

Nakladatel

AMER INST PHYSICS

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

Obecná matematika

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

URL

Kód RIV

RIV/46747885:24510/13:#0001130

Organizace

Fakulta přírodovědně-humanitní a pedagogická – Technická univerzita v Liberci – Repozitář

ISBN

978-0-7354-1198-2

ISSN

DOI

http://dx.doi.org/10.1063/1.4854760

UT WoS

000346051300025

Klíčová slova anglicky

Discontinuous Galerkin method; Black-Scholes equation; space semidiscretization; nonsymmetric stabilization of diffusion terms; upwinding; a priori error estimates; experimental order of convergence

Změněno: 3. 4. 2015 10:58, Jiří Hozman

Anotace

V originále

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

Citovat

HOZMAN, Jiří. Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem. Online. In Pasheva, V; Venkov, G. 39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE13), AIP Conference Proceedings 1570. Melville, NY, USA: AMER INST PHYSICS, 2013, s. 227-234. ISBN 978-0-7354-1198-2. Dostupné z: https://dx.doi.org/10.1063/1.4854760.

@inproceedings{18200,
   author = {Hozman, Jiří},
   address = {Melville, NY, USA},
   booktitle = {39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE13), AIP Conference Proceedings 1570},
   doi = {http://dx.doi.org/10.1063/1.4854760},
   editor = {Pasheva, V; Venkov, G},
   keywords = {Discontinuous Galerkin method; Black-Scholes equation; space semidiscretization; nonsymmetric stabilization of diffusion terms; upwinding; a priori error estimates; experimental order of convergence},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Melville, NY, USA},
   isbn = {978-0-7354-1198-2},
   pages = {227-234},
   publisher = {AMER INST PHYSICS},
   title = {Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem},
   url = {http://dx.doi.org/10.1063/1.4854760},
   year = {2013}
}

TY  - CONF
ID  - 18200
AU  - Hozman, Jiří
PY  - 2013
TI  - Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem
PB  - AMER INST PHYSICS
CY  - Melville, NY, USA
SN  - 9780735411982
KW  - Discontinuous Galerkin method
KW  - Black-Scholes equation
KW  - space semidiscretization
KW  - nonsymmetric stabilization of diffusion terms
KW  - upwinding
KW  - a priori error estimates
KW  - experimental order of convergence
UR  - http://dx.doi.org/10.1063/1.4854760
L2  - http://dx.doi.org/10.1063/1.4854760
N2  - In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.
ER  -

HOZMAN, Jiří. Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem. Online. In Pasheva, V; Venkov, G. \textit{39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE13), AIP Conference Proceedings 1570}. Melville, NY, USA: AMER INST PHYSICS, 2013, s.~227-234. ISBN~978-0-7354-1198-2. Dostupné z: https://dx.doi.org/10.1063/1.4854760.