zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Mathematical analysis and numerical methods for a partial differential equations model governing a ratchet cap pricing in the LIBOR market model. (English) Zbl 1222.91061
Summary: We present a mathematical model for pricing a particular financial product: the ratchet cap. This derivative product depends on certain interest rates (whose dynamics we assume that follow the LIBOR market model). The pricing model is rigorously posed in terms of a sequence of nested Cauchy problems associated to uniformly parabolic partial differential equations. First, for each problem the existence and uniqueness of solution is obtained. Next, this analysis allows to propose a new and more efficient numerical method based on the approximation by computable fundamental solutions of constant coefficient operators. The advantage in terms of computational time of this new modeling and analytically based approach is illustrated by comparison with the classically used Monte Carlo simulation and a characteristics Crank-Nicolson time discretization combined with finite elements strategy.
91G20Derivative securities
91G30Interest rates (stochastic models)
35A35Theoretical approximation to solutions of PDE
35K15Second order parabolic equations, initial value problems
65M25Method of characteristics (IVP of PDE, numerical methods)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35A08Fundamental solutions of PDE