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Title: The $dX(t)=Xb(X)dt+X\sigma(X)dW$ equation and financial mathematics. I (English)
Author: Štěpán, Josef
Author: Dostál, Petr
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 39
Issue: 6
Year: 2003
Pages: [653]-680
Summary lang: English
Category: math
Summary: The existence of a weak solution and the uniqueness in law are assumed for the equation, the coefficients $b$ and $\sigma $ being generally $C({\mathbb{R}}^+)$-progressive processes. Any weak solution $X$ is called a $(b,\sigma )$-stock price and Girsanov Theorem jointly with the DDS Theorem on time changed martingales are applied to establish the probability distribution $\mu _\sigma $ of $X$ in $C({\mathbb{R}}^+)$ in the special case of a diffusion volatility $\sigma (X,t)=\tilde{\sigma }(X(t)).$ A martingale option pricing method is presented. (English)
Keyword: weak solution and uniqueness in law in the SDE-theory
Keyword: $(b,\sigma )$-stock price
Keyword: its Girsanov and DDS-reduction
Keyword: investment process
Keyword: option pricing
MSC: 60H10
MSC: 91B28
MSC: 91G20
idZBL: Zbl 1249.91128
idMR: MR2035643
Date available: 2009-09-24T19:57:50Z
Last updated: 2015-03-24
Stable URL:
Related article:
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