Quadratic optimal functional quantization of stochastic processes and numerical applications

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a Hilbert-valued random variable, using a nearest neighbour projection on a finite codebook. A special emphasis is made on the computational aspects and the numerical applications, in particular the pricing of some path-dependent European options.Comment: 41 page

Explicit-implicit methods with applications to banach space valued functions in abstract fractional calculus

Explicit iterative methods have been used extensively to generate a sequence approximating a solution of an equation on a Banach space setting

Equations for banach space valued functions in fractional vector calculi

The aim of this chapter is to solve equations on Banach space using iterative methods under generalized conditions. The differentiability of the operator involved is not assumed and its domain is not necessarily convex. Several applications are suggested including Banach space valued functions of abstract fractional calculus, where all integrals are of Bochner-type. It follows [5]

Generating sequences for solving in abstract g-fractional calculus

The aim of this chapter is to utilize proper iterative methods for solving equations on Banach spaces

Semi-local convergence in right abstract fractional calculus

We provide a semi-local convergence analysis for a class of iterative methods under generalized conditions in order to solve equations in a Banach space setting. Some applications are suggested including Banach space valued functions of right fractional calculus, where all integrals are of Bochner-type. It follows [5]