Derivation of the drift diffusion Shockley-Read-Hall model for semiconductors
Derivation of the Zakharov equations
Determination of surfaces in three-dimensional Minkowski and Euclidean spaces based on solutions of the sinh-Laplace equation.
Deterministic state-constrained optimal control problems without controllability assumptions
In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position x. In the constrained...
Deterministic state-constrained optimal control problems without controllability assumptions
In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position x. In...
Development of a mathematical theory of inner gravitational waves in deep reservoirs of variable width.
Development of local, global, and trace estimates for the solutions of elliptic equations.
Développement asymptotique de la densité d'états pour l'opérateur de Schrödinger aléatoire avec champ magnétique
Développements asymptotiques dans l'approximation de Born-Oppenheimer
Développements asymptotiques et effet tunnel dans l'approximation de Born-Oppenheimer
Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique
DG method for numerical pricing of multi-asset Asian options—the case of options with floating strike
Option pricing models are an important part of financial markets worldwide. The PDE formulation of these models leads to analytical solutions only under very strong simplifications. For more general models the option price needs to be evaluated by numerical techniques. First, based on an ideal pure diffusion process for two risky asset prices with an additional path-dependent variable for continuous arithmetic average, we present a general form of PDE for pricing of Asian option contracts on two...
DG method for pricing European options under Merton jump-diffusion model
Under real market conditions, there exist many cases when it is inevitable to adopt numerical approximations of option prices due to non-existence of analytical formulae. Obviously, any numerical technique should be tested for the cases when the analytical solution is well known. The paper is devoted to the discontinuous Galerkin method applied to European option pricing under the Merton jump-diffusion model, when the evolution of the asset prices is driven by a Lévy process with finite activity....
DG method for the numerical pricing of two-asset European-style Asian options with fixed strike
The evaluation of option premium is a very delicate issue arising from the assumptions made under a financial market model, and pricing of a wide range of options is generally feasible only when numerical methods are involved. This paper is based on our recent research on numerical pricing of path-dependent multi-asset options and extends these results also to the case of Asian options with fixed strike. First, we recall the three-dimensional backward parabolic PDE describing the evolution of European-style...
DGM for real options valuation: Options to change operating scale
The real options approach interprets a flexibility value, embedded in a project, as an option premium. The object of interest is to valuate real options to change operating scale, typical for natural resources industry. The evolution of the project as well as option prices is decribed by partial differential equations of the Black-Scholes type, linked through a payoff function given by a type of the flexibility provided. The governing equations are discretized by the discontinuous Galerkin method...
Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. Teil III.
Difference schemes for pluriparabolic equations.
Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation
We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup does exist for any bounded ; and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given.
Differential Geometry of Real Monge-Ampère Foliations.
Diffusion classique et quantique par un trou noir en formation