dc.contributor.author |
Kushpel, Alexander
|
|
dc.date.accessioned |
2020-04-29T21:40:40Z |
|
dc.date.available |
2020-04-29T21:40:40Z |
|
dc.date.issued |
2019-03-20 |
|
dc.identifier.citation |
Kushpel, Alexander, "A method of inversion of Fourier transforms and its applications", International Journal of Differential Equations and Applications, Vol. 18, No. 1, pp. 25-29, (2019). |
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dc.identifier.issn |
1311-2872 |
|
dc.identifier.issn |
1314-6084 |
|
dc.identifier.uri |
http://hdl.handle.net/20.500.12416/3510 |
|
dc.description.abstract |
The problem of inversion of Fourier transforms is a frequently discussed topic in the
theory of PDEs, Stochastic Processes and many other branches of Analysis. We consider
here in more details an application of a method proposed in Financial Modeling. As
a motivating example consider a frictionless market with no arbitrage opportunities
and a constant riskless interest rate r > 0. Assuming the existence of a risk-neutral
equivalent martingale measure Q, we get the option value V = e
−rTE
Q[ϕ] at time 0
and maturity T > 0, where ϕ is a reward function and the expectation E
Q is taken with
respect to the equivalent martingale measure Q. Usually, the reward function ϕ has a
simple structure. Hence, the main problem is to approximate properly the respective
density function and then to approximate E
Q [ϕ]. Here we offer an approximant for
the density function without proof of any convergence results. These problems will be
considered in details in our future publications. |
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dc.language.iso |
eng |
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dc.publisher |
Academic Publications LTD |
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dc.rights |
info:eu-repo/semantics/openAccess |
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dc.subject |
Fourier Transform |
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dc.subject |
PDE |
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dc.subject |
Sk-Spline |
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dc.subject |
L´Evy Process |
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dc.subject |
Density Function |
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dc.title |
A method of inversion of Fourier transforms and its applications |
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dc.type |
article |
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dc.relation.journal |
International Journal of Differential Equations and Applications |
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dc.contributor.authorID |
279144 |
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dc.identifier.volume |
18 |
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dc.identifier.issue |
1 |
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dc.identifier.startpage |
25 |
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dc.identifier.endpage |
29 |
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dc.contributor.department |
Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü |
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