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 …

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 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 …

For non-storable commodities forward looking information about market conditions is not
necessarily incorporated in today's prices, and the standard assumption that the information …

We introduce the forward integral with respect to a pure jump Lévy process and prove an Itô
formula for this integral. Then we use Mallivin calculus to establish a relationship between …

In physics, classical analysis plays a central role. For instance in Newtonian mechanics,
thermodynamics, and electricity, many phenomena are well explained by deterministic …

We consider a financial market driven by a Lévy process with filtration. An insider in this
market is an agent who has access to more information than an honest trader …

The background for the general mathematical link between utility and information theory
investigated in this paper is a simple financial market model with two kinds of small traders …

We study a controlled stochastic system whose state is described by a stochastic differential
equation with anticipating coefficients. This setting is used to model markets where insiders …

In order to increase overall transparency on key operational information, power transmission
system operators publish an increasing amount of fundamental data, including forecasts of …