Chaotic solution for the Black-Scholes equation

DOI10.1090/S0002-9939-2011-11069-4zbMath1238.47051OpenAlexW2025880370MaRDI QIDQ2884425

Jerome A. Goldstein, Gisèle Ruiz Goldstein, Hassan Emamirad

Publication date: 29 May 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-11069-4

zbMATH Keywords

Black-Scholes equationhypercyclic and chaotic semigroup

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Financial applications of other theories (91G80) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Cyclic vectors, hypercyclic and chaotic operators (47A16) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)

Related Items (18)

Universal properties of the isotropic Laplace operator on homogeneous trees ⋮ Distributionally chaotic families of operators on Fréchet spaces ⋮ The Null Volatility Limit of the Chaotic Black-Scholes Equation ⋮ Identifying initial condition in degenerate parabolic equation with singular potential ⋮ A generalized Cox-Ingersoll-Ross equation with growing initial conditions ⋮ Frequently hypercyclic translation semigroups ⋮ A class of quasicontractive semigroups acting on Hardy and weighted Hardy spaces ⋮ Identification of an unknown spatial source function in a multidimensional hyperbolic partial differential equation with interior degeneracy ⋮ The specification property for \(C_0\)-semigroups ⋮ Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Non Smooth Parabolic Equations ⋮ Chaotic \(C_0\)-semigroups induced by semiflows in Lebesgue and Sobolev spaces ⋮ A simple characterization of chaos for weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces ⋮ Unnamed Item ⋮ F-hypercyclic operators on Fréchet spaces ⋮ Frequently hypercyclic and chaotic behavior of some first-order partial differential equation ⋮ New approach to identify the initial condition in degenerate hyperbolic equation ⋮ Strong mixing measures for \(C_0\)-semigroups ⋮ Distributional chaos for the forward and backward control traffic model

Cites Work

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• Operators with dense, invariant, cyclic vector manifolds
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• A semigroup approach to American options
• Chaos for functions of discrete and continuous weighted shift operators
• Polynomials of Generators of Integrated Semigroups
• Chaos in Linear Distributed Systems
• TOPOLOGICAL CHAOS FOR A CLASS OF LINEAR MODELS
• Universal families and hypercyclic operators
• Hypercyclic and chaotic semigroups of linear operators
• Some Remarks on Infinitesimal Generators of Analytic Semigroups
• Abstract Evolution Equations

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