13 papers
The stochastic fractional transport heat equation
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Øksendal
We give an introduction to the time-fractional stochastic heat equation driven by 1+d-parameter fractional time-space white noise, in the following two cases: (i) With additive fra…
A time-fractional Kalman filter
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Øksendal +1
We study a linear filtering problem in which the signal process is described by a time-fractional linear stochastic differential equation driven by Brownian motion. We derive a sto…
Efficient Computation Of Sensitivities For Derivatives In Energy Markets
Fred Espen Benth, Olfa Draouil, Farouk Hammami
In this study, we develop a stochastic framework for computing Delta sensitivities in energy markets, where both prices and traded volumes are modeled as correlated stochastic proc…
Multiparameter Lévy white noise theory and applications
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Øksendal
We construct a white noise theory and white noise calculus for the (multi-parameter) L\' evy sheet and its compensated Poisson random measures. The theory applies to stochastic par…
The stochastic heat inclusion with fractional time driven by time-space Brownian and Lévy white noise
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Øksendal
We study a time-fractional stochastic heat inclusion driven by additive time-space Brownian and Lévy white noise. The fractional time derivative is interpreted as the Caputo deriva…
A new approach to optimal stopping for Hunt processes
Achref Bachouch, Olfa Draouil, Bernt Øksendal
In this paper we present a new verification theorem for optimal stopping problems for Hunt processes. The approach is based on the Fukushima-Dynkin formula, and its advantage is th…
Viable Insider Markets
Olfa Draouil, Bernt Øksendal
We consider the problem of optimal inside portfolio in a financial market with a corresponding wealth process modelled by \begin{align}\label{eq0.1} \begin{cas…
Optimal insider control of stochastic Volterra equations
Olfa Draouil
We study the problem of optimal inside control of a stochastic Volterra equation driven by a Brownian motion and a Poisson random measure. We prove a sufficient and a necessary max…
A white noise approach to optimal insider control of systems with delay
Olfa Draouil, Bernt Øksendal
We use a white noise approach to study the problem of optimal inside control of a stochastic delay equation driven by a Brownian motion B and a Poisson random measure N. In particu…
Optimal insider control of stochastic partial differential equations
Olfa Draouil, Bernt Øksendal
We study the problem of optimal inside control of an SPDE (a stochastic evolution equation) driven by a Brownian motion and a Poisson random measure. Our optimal control problem is…
Optimal insider control and semimartingale decompositions under enlargement of filtration
Olfa Draouil, Bernt Øksendal
We combine stochastic control methods, white noise analysis and Hida-Malliavin calculus applied to the Donsker delta functional to obtain new representations of semimartingale deco…
Stochastic differential games with inside information
Olfa Draouil, Bernt Øksendal
We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noi…
A Donsker delta functional approach to optimal insider control and applications to finance
Olfa Draouil, Bernt Øksendal
We study \emph{optimal insider control problems}, i.e. optimal control problems of stochastic systems where the controller at any time in addition to knowledge about the histor…