5 Stochastic Differential Equations Page 1 5 Stochastic Differential Equations 5.1 Examples
and Some Solution Methods We now return to the possible solutions Xt(ω) of the stochastic …

Fractional Brownian motion (fBm) has been widely used to model a number of phenomena
in diverse fields from biology to finance. This huge range of potential applications makes …

This volume examines the theory of fractional Brownian motion and other long-memory
processes. Interesting topics for PhD students and specialists in probability theory …

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 …

The purpose of this paper is to develop a fractional white noise calculus and to apply this to
markets modeled by (Wick–) Itô type of stochastic differential equations driven by fractional …

We present a new framework for fractional Brownian motion in which processes with all
indices can be considered under the same probability measure. Our results extend recent …

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 monograph is an introduction to some aspects of stochastic analysis in the framework of
normal martingales, in both discrete and continuous time. The text is mostly self-contained …

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 …

In a market driven by a Lévy martingale, we consider a claim ξ. We study the problem of
minimal variance hedging and we give an explicit formula for the minimal variance portfolio …