Spectral Approximation of Infinite-Dimensional Black-Scholes Equations with Memory

This paper considers the pricing of a European option using a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary price structures described by the authors of this paper (1999). Under the smoothness assumption of the payoff function, it is shown that...

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Vydané v:International journal of stochastic analysis Ročník 2009; číslo 1
Hlavní autori: Chang, Mou-Hsiung, Youree, Roger K.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Hindawi Publishing Corporation 01.01.2009
Hindawi Limited
Predmet:
Bank accounts
Derivatives
Mathematical functions
Mathematical models
Partial differential equations
Studies
ISSN:1048-9533, 2090-3332, 1687-2177, 2090-3340
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Shrnutí:This paper considers the pricing of a European option using a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary price structures described by the authors of this paper (1999). Under the smoothness assumption of the payoff function, it is shown that the infinite dimensional Black-Scholes equation possesses a unique classical solution. A spectral approximation scheme is developed using the Fourier series expansion in the space C[−h,0] for the Black-Scholes equation. It is also shown that the nth approximant resembles the classical Black-Scholes equation in finite dimensions.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1048-9533
2090-3332
1687-2177
2090-3340
DOI:10.1155/2009/782572