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Entropic Conditions and Hedging

Samuel Njoh (2007)

ESAIM: Probability and Statistics

In many markets, especially in energy markets, electricity markets for instance, the detention of the physical asset is quite difficult. This is also the case for crude oil as treated by Davis (2000). So one can identify a good proxy which is an asset (financial or physical) (one)whose the spot price is significantly correlated with the spot price of the underlying (e.g. electicity or crude oil). Generally, the market could become incomplete. We explicit exact hedging strategies for exponential...

Équations de transport dont les vitesses sont partiellement B V

Nicolas Lerner (2003/2004)

Séminaire Équations aux dérivées partielles

Nous démontrons l’unicité des solutions faibles pour une classe d’équations de transport dont les vitesses sont partiellement à variations bornées. Nous nous intéressons à des champs de vecteurs du type a 1 ( x 1 ) · ∂ x 1 + a 2 ( x 1 , x 2 ) · ∂ x 2 , a 1 ∈ B V ( ℝ x 1 N 1 ) , a 2 ∈ L x 1 1 B V ( ℝ x 2 N 2 ) , avec une borne sur la divergence de chacun des champs a 1 , a 2 . Ce modèle a été étudié récemment dans [LL] par C. Le Bris et P.-L. Lions avec une régularité W 1 , 1  ; nous montrons ici également que, dans le cas W 1 , 1 , le contrôle L ∞ de la divergence totale du champ est suffisant. Notre méthode consiste à démontrer...

Estimations of noncontinuable solutions of second order differential equations with p -Laplacian

Eva Pekárková (2010)

Archivum Mathematicum

We study asymptotic properties of solutions for a system of second differential equations with p -Laplacian. The main purpose is to investigate lower estimates of singular solutions of second order differential equations with p -Laplacian ( A ( t ) Φ p ( y ' ) ) ' + B ( t ) g ( y ' ) + R ( t ) f ( y ) = e ( t ) . Furthermore, we obtain results for a scalar equation.

Existence and positivity of solutions for a nonlinear periodic differential equation

Ernest Yankson (2012)

Archivum Mathematicum

We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.

Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.

Lucie Baudouin (2005)

Revista Matemática Complutense

We study an Helium atom (composed of one nucleus and two electrons) submitted to a general time dependent electric field, modeled by the Hartree-Fock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, for the position of the nucleus. We prove a result of existence and regularity for the Cauchy problem, where the main ingredients are a preliminary study of the regularity in a nonlinear Schrödinger equation with semi-group techniques and...

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