Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$. In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noise parameter is obtained. The...

We study the BPE (Brownian particle equation) model of the Burgers equation presented in the preceeding article [6]. More precisely, we are interested in establishing the existence and uniqueness properties of solutions using probabilistic techniques.

In this paper we consider an insider with privileged information that is affected by an independent noise vanishing as the revelation time approaches. At this time, information is available to every trader. Our financial markets are based on Wiener space. In probabilistic terms we obtain an...

We develop a general error analysis framework for the Monte Carlo simulation of densities for functionals in Wiener space. We also study variance reduction methods with the help of Malliavin derivatives. For this, we give some general heuristic principles which are applied to diffusion...

We study the existence of moments and the tail behaviour of the densities of storage processes. We give sufficient conditions for existence and non-existence of moments using the integrability conditions of submultiplicative functions with respect to Lévy measures. Then, we study the...

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative...

We introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the...

This paper studies the rate of convergence of an appropriate discretization scheme of the solution of the Mc Kean-Vlasov equation introduced by Bossy and Talay. More specifically, we consider approximations of the distribution and of the density of the solution of the stochastic differential...