Curso introductorio al cálculo de Malliavin, teoría del ruido blanco y sus aplicaciones.

SPEAKER: Bernt Øksendal (Universitetet i Oslo)

DATE: Wednesday 9 May 2018 / 10:30 - 12:30 h

VENUE: Aula 520, Módulo 17, Departamento de Matemáticas, UAM(Campus de Cantoblanco, Madrid)

ABSTRACT: The Hida theory of white noise has proved to be a powerful tool in stochastic calculus. An
example is the celebrated Clark-Ocone formula, which is important in mathematical finance.
Moreover, white noise calculus has the advantage that it also works when dealing with issues beyond
the semi-martingale context, for example insider control, control of stochastic Volterra equations etc.
In these lectures we first give a brief introduction to the Hida white noise theory, extended to Lévy
processes and calculus with Wick products and Hida-Malliavin derivatives. Then we apply this
calculus to study some optimal control problems in finance.
The presentation is partly based on joint works with Nacira Agram, Olfa Draouil and Elin Røse, all at
the Department of Mathematics, University of Oslo, Norway and Samia Yakhlef, University of Biskra,
Algeria. The most relevant papers are listed below.
[1] O. Draouil and B.Øksendal: “A Donsker delta functional approach to optimal insider control and
applications to finance.” Comm. Math. Stat. (CIMS) 3 (2015), 365-421.DOI 10.1007/s40304-015-0065-y
Erratum: Comm. Math. Stat. (CIMS) 3 (2015), 535-540. DOI 10.1007/s40304-015-0074-x
http://arxiv.org/abs/1504.02581
[2] B. Øksendal and E. Røse: “A white noise approach to insider trading”. In T. Hida and L. Streit
(editors): “Let Us Use White Noise”. World Scientific, Singapore (2017), pp. 191-203.
http://arxiv.org/abs/1508.06376
[3] N. Agram and B. Øksendal: “A Hida-Malliavin white noise calculus approach to optimal control.” 3
May 2017. http://arxiv.org/abs/1704.08899v2
[4] N. Agram, B. Øksendal and S. Yakhlef: “New approach to optimal control of stochastic Volterra
integral equations”. 8 March 2018. arXiv:1709.05463v2
minicourse
AN INTRODUCTION TO WHITE NOISE
THEORY AND HIDA-MALLIAVIN CALCULUS,
WITH APPLICATIONS TO FINANCE
APPLIED MATHEMATICS
UNIVERSIDAD