Related papers: An introduction to Malliavin calculus
In this paper, we describe an explicit extension formula in sensitivity analysis regarding the Malliavin weight for jump-diffusion mean-field stochastic differential equations whose local Lipschitz drift coefficients are influenced by the…
In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the…
An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional…
This short review is an introduction to a great variety of methods, the collection of which is called the Painlev\'e analysis, intended at producing all kinds of exact (as opposed to perturbative) results on nonlinear equations, whether…
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
Every calculus student learns Cavalieri's quadrature formula for the antiderivative of x^n (integer n). We observe here that the logarithmic (n=-1) case implies all the others.
The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The…
In recent years there has been an advent of quanto options in energy markets. The structure of the payoff is rather a different type from other markets since it is written as a product of an underlying energy index and a measure of…
We discuss the problem of possible boundary terms at poles of the drift in the complex Langevin method, which spoil correctness of the method. For the simplest, however paradigmatic cases we can find complete answers. Lessons for more…
This papers develops a stochastic integration theory with respect to volatility modulated L\'{e}vy-driven Volterra (VMLV) processes. It extends recent results in the literature to allow for stochastic volatility and pure jump processes in…
Leibniz's rule for the $n$-th derivative of a product is a very well known and extremely useful formula. In this article, we introduce an analogous explicit formula for the $n$-th derivative of a quotient of two functions. Later, we use…
Some formal analogies between the Differential Calculus in One Variable and the Differential Calculus in Several Variables are presented. It is studied and introduced the derivability of functions at several variables from the single…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.
Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.
This survey discusses the classical Bernstein and Markov inequalities for the derivatives of polynomials, as well as some of their extensions to general sets.
We study quasi-linear stochastic partial differential equations with discontinuous drift coefficients. Existence and uniqueness of a solution is already known under weaker conditions on the drift, but we are interested in the regularity of…
In this note we discuss a variant of linear logic with idempotent exponential modalities. We propose a sequent calculus system and discuss its semantics. We also give a concrete relational model for this calculus.