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SSRN Electronic Journal, 2021
The Local Stochastic Volatility model is the main model used to take into account the correct pricing and hedging with the volatility dynamic. We introduce a new methodology that combines Singular perturbation analysis and exotic greek computation. We obtain asymptotic formulae for the LSV impact which work extremely well. Tests are performed on the
Florian Monciaud, Adil Reghai
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The Local Stochastic Volatility model is the main model used to take into account the correct pricing and hedging with the volatility dynamic. We introduce a new methodology that combines Singular perturbation analysis and exotic greek computation. We obtain asymptotic formulae for the LSV impact which work extremely well. Tests are performed on the
Florian Monciaud, Adil Reghai
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Singular Perturbations in Manufacturing
SIAM Journal on Control and Optimization, 1993Summary: An asymptotic analysis for a large class of stochastic optimization problems arising in manufacturing is presented. A typical example of the problems considered in this paper is a production planning problem with random capacity and demand.
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NAIVE SINGULAR PERTURBATION THEORY
Mathematical Models and Methods in Applied Sciences, 2001The paper demonstrates, via extremely simple examples, the shocks, spikes, and initial layers that arise in solving certain singularly perturbed initial value problems for first-order ordinary differential equations. As examples from stability theory, they are basic to many asymptotic techniques.
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Corner singularities and singular perturbations
ANNALI DELL UNIVERSITA DI FERRARA, 2001Summary: A corner singularity expansion is developed for a singularly perturbed elliptic boundary value problem. The problem is set in a sector of the plane. In the expansion, particular attention is paid to the singular perturbation parameter. The result is used to give pointwise bounds on derivatives of the solution.
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Singular perturbation potentials
Annals of Physics, 1977Abstract This is a perturbative analysis of the eigenvalues and eigenfunctions of Schrodinger operators of the form −Δ + A + λV, defined on the Hilbert space L2(Rn), where Δ = Σ i=1 n ∂ 2 ∂X i 2 , A is a potential function and V is a positive perturbative potential function which diverges at some finite point ...
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2020
In this chapter the topological asymptotic analysis of the energy shape functional associated with the Poisson’s equation, with respect to singular domain perturbations, is formally developed. In particular, we consider singular perturbations produced by the nucleation of small circular holes endowed with homogeneous Neumann, Dirichlet, or Robin ...
Antonio André Novotny, Jan Sokołowski
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In this chapter the topological asymptotic analysis of the energy shape functional associated with the Poisson’s equation, with respect to singular domain perturbations, is formally developed. In particular, we consider singular perturbations produced by the nucleation of small circular holes endowed with homogeneous Neumann, Dirichlet, or Robin ...
Antonio André Novotny, Jan Sokołowski
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Semilinear singular perturbation
Nonlinear Analysis: Theory, Methods & Applications, 1995A second-order periodic boundary value problem is considered. The method of upper and lower solutions is applied to prove the existence of a solution.
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Singular Perturbation Problems
1951The equations considered in this rarer are linear differential equations in one and two independent variables. The problem at hand is to study solutions of boundary value problems for these equations in their dependence on a small parameter ϵ. Specifically, the equations are of the form (A) ϵ Nɸ + Mɸ = 0 where M, N are linear differential expressions,
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2016
In this chapter we deal with perturbations whose influence is concentrated outside of the domain of essential self-adjointness of the free Hamiltonian. We show that the extended rigged spaces method is applicable to such perturbations. A new step is the introduction of the scale of Hilbert spaces and involving in the consideration the unperturbed ...
Volodymyr Koshmanenko, Mykola Dudkin
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In this chapter we deal with perturbations whose influence is concentrated outside of the domain of essential self-adjointness of the free Hamiltonian. We show that the extended rigged spaces method is applicable to such perturbations. A new step is the introduction of the scale of Hilbert spaces and involving in the consideration the unperturbed ...
Volodymyr Koshmanenko, Mykola Dudkin
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Singular Perturbation Problems
2004In this chapter the problems when the small parameter stands by a highest order derivatives are considered. Note that for e = 0 a qualitative change of the system occurs since the system order of the analysed differential equation is decreased. The similar like asymptotics is called the singular one.
I. Andrianov +2 more
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