We give a survey of the stochastic calculus of fractional Brownian motion, and we discuss its applications to financial markets where the prices are described as solutions of stochastic differential equations driven by ...

We give a short introduction to the white noise theory for multiparameter Lévy processes and its application to stochastic partial differential equations driven by such processes. Examples include temperature distribution ...

We present various versions of the maximum principle for optimal control of forward-backward SDEs with jumps. Our study is motivated by risk minimization via g-expectations. We first prove a general sufficient maximum ...

In this paper we first deal with the problem of optimal control for zero-sum stochastic differential games. We give a necessary and sufficient maximum principle for that problem with partial information. Then we use the ...

In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic ...

In this paper we consider a general partial information stochastic differential game where the state process is a controlled Itô-Lévy process. We use Malliavin calculus to derive a maximum principle for general stochastic ...