These lecture notes cover a major part of the crash course on financial modeling with jump
processes given by the author in Bologna on May 21–22, 2009. After a brief introduction, we …

Fix a domain\mathcal S ⊂ R^ k (our solvency region) and let Y (t)= Y^(u)(t) be a stochastic
process of the form d Y (t) &= b (Y (t), u (t)) d t+ σ (Y (t), u (t)) d B (t)\nonumber\&\quad+ ∫ …

The story of modelling financial markets with stochastic processes began in 1900 with the
study of Bachelier (1900). He modelled stocks as a Brownian motion with drift. However, the …

The purpose of this chapter is to present an overview of recent results on stochastic control,
in particular, portfolio optimization, achieved via techniques of Malliavin calculus and …

Stochastic Calculus of Variations (or Malliavin Calculus) consists, in brief, in constructing
and exploiting natural differentiable structures on abstract probability spaces; in other words …

This paper considers a mean-field type stochastic control problem where the dynamics is
governed by a controlled Itô–Lévy process and the information available to the controller is …

We construct a white noise theory for Lévy processes. The starting point of this theory is a
chaos expansion for square integrable random variables. We use this approach to Malliavin …

We provide a new characterization of mean-variance hedging strategies in a general
semimartingale market. The key point is the introduction of a new probability measure P⋆ …

Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic
volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact …

A suitable canonical Lévy process is constructed in order to study a Malliavin calculus based
on a chaotic representation property of Lévy processes proved by Itô using multiple two …