zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A note on Wick products and the fractional Black-Scholes model. (English) Zbl 1092.91021
The purpose of the paper is to discuss precisely whether new concepts connected with financial market driven by a fractional Brownian motion are reasonable from the economic point of view. The authors compare concepts of the Wick product and self-financing introduced by R. J. Elliott and J. van der Hoek [Math. Finance 13, No. 2, 301–330 (2003; Zbl 1069.91047)] and Y. Hu and B. Øksendal [Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6, No. 1, 1–32 (2003; Zbl 1045.60072)]. The conclusion is unfavourable: the definition of Wick-financing portfolios used by Elliott-van der Hoek has no economic interpretation as a self-financing condition. Also, if one insists to use their pricing theory for trading purposes, then it will in some cases lead to easily implementable naive arbitrage opportunities for the counterpart. The same, replacing the standard definition of portfolio value by the Wick one as in Hu-Øksendal papers cannot be motivated from the economic point of view. The reasons are given. As a conclusion, the authors claim that in general no reasons against FBM in finance and their criticism does not extend to all the financial interpretations of models with FBM.

MSC:
91B28Finance etc. (MSC2000)
60H05Stochastic integrals