Linear stochastic parabolic equations, degenerating on the boundary of a domain.
Lototsky, Sergey V. (2001)
Electronic Journal of Probability [electronic only]
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Displaying similar documents to “Variational analysis for the Black and Scholes equation with stochastic volatility”
Linear stochastic parabolic equations, degenerating on the boundary of a domain.
On the discretization in time of parabolic stochastic partial differential equations
Jacques Printems (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We first generalize, in an abstract framework, results on the order of convergence of a semi-discretization in time by an implicit Euler scheme of a stochastic parabolic equation. In this part, all the coefficients are globally Lipchitz. The case when the nonlinearity is only locally Lipchitz is then treated. For the sake of simplicity, we restrict our attention to the Burgers equation. We are not able in this case to compute a pathwise order of the approximation, we introduce the weaker...
Fast deterministic pricing of options on Lévy driven assets
Ana-Maria Matache, Tobias Von Petersdorff, Christoph Schwab (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Arbitrage-free prices of European contracts on risky assets whose log-returns are modelled by Lévy processes satisfy a parabolic partial integro-differential equation (PIDE) . This PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the -scheme in time and a wavelet Galerkin method with degrees of freedom in log-price space. The dense matrix for can be replaced by a sparse matrix in the wavelet basis,...
Support of a Marcus equation in dimension 1.
Simon, Thomas (2000)
Electronic Communications in Probability [electronic only]
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Analysis of an uncertain volatility model.
Di Francesco, Marco, Foschi, Paolo, Pascucci, Andrea (2006)
Journal of Applied Mathematics and Decision Sciences
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A 2-dimensional SDE whose solutions are not unique.
Swart, Jan M. (2001)
Electronic Communications in Probability [electronic only]
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Variational Analysis for the Black and Scholes Equation with Stochastic Volatility
Yves Achdou, Nicoletta Tchou (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a...