Seminar lecture by Dr. Asma Khedher, University of Amsterdam

Dr. Asma Khedher from University of Amsterdam will give a seminar lecture with the title:

Ornstein-Uhlenbeck processes and affine stochastic volatility models in Hilbert spaces. 

First, we present a model for the instantaneous variance of an Hilbert space valued Ornstein-Uhlenbeck process (OU process), with dynamics given by a stochastic partial differential equation (SPDE). This model allows for a stochastic volatility with state dependent jumps. The existence of an appropriate variance process will be deduced from the existence of infinitely divisible processes on the cone of positive-definite Hilbert-Schmidt operators and by solving an associated class of ordinary differential equations, allowing for a reconstruction of the Lévy-Khintchine exponent of the variance process. 

Second, we extend the Wishart processes to Hilbert-Schmidt operator framework. 

This is based on a work in progress with Sonja Cox, Christa Cuchiero, and Sven Karbach.

Published May 24, 2019 2:30 PM - Last modified May 31, 2019 10:29 AM