Seminar in applied mathematics and statistics
SPEAKER: Sascha Desmettre (Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz).
TITLE: Rough Volatility Modeling and Portfolio Optimization.
ABSTRACT: This talk gives an introduction to the theory of rough paths with a focus on financial mathematics. These concepts are then applied for the modeling of a financial market with stochastic dynamics for the volatility. In particular, the stochastic volatility model of Heston is investigated and extended to fractional and rough market dynamics, which are obtained by applying the Riemann-Liouville fractional integral operator and the Marchaud fractional derivative to the classical Cox-Ingersoll-Ross process, respectively. Using a suitable representation, followed by a reasonable quantization of the underlying probability measures, we show that it is possible to cast the problem into the classical stochastic control framework. We deduce a Feynman-Kac representation for these fractional and rough market models and solve the corresponding continuous time portfolio optimization problems.
Upcoming events (after November 20):
Wednesday, November 27 at 15.15: Jesper Møller
Wednesday, February 19 at 15.15: Budhi Surya