| 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:
|
http://hdl.handle.net/10338.dmlcz/135564 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/135565 |
| . |
| Reference:
|
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| Reference:
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