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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 maximum principle...
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 maximum principle...
There are two mathematical models of elastic walls of healthy and atherosclerotic blood
vessels developed and studied. The models are included in a numerical model of global
blood circulation via recovery of the vessel wall state equation. The joint model allows
us to study the impact of arteries atherosclerotic disease of a set of arteries on
regional haemodynamics.
We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...
We present a new methodology for the numerical resolution of the hydrodynamics
of incompressible viscid newtonian fluids. It is based on the Navier-Stokes
equations and we refer to it as the vorticity projection method.
The method is robust enough to handle complex and convoluted configurations
typical to the motion of biological structures in viscous fluids.
Although the method is applicable to three dimensions, we address here
in detail only the two dimensional case. We provide numerical data...
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