The course will be focused on the analysis of
affine and polynomial processes. Particular emphasis will be given to the study of their infinite dimensional versions, which take values in (signed) measures or functions spaces. This allows to consider applications ranging from rough volatility models over non-linear PDEs, to stochastic portfolio theory.
Time table:
Monday 25: 9.30 -11.30 (Room G)
Wednesday 27: 13.30-16.30 (Room M)
Thursday 28: 12.30 - 14.30 ( Room Tessari)
References:
E. Abi Jaber and O. E. Euch. Multi-factor approximation of rough volatility models. Preprint,
available at arXiv:1801.10359, 2018.
E. Abi Jaber, M. Larsson, and S. Pulido. Affi ne Volterra processes. Preprint, available at
arXiv:1708.08796, 2017.
C. Cuchiero, D. Filipovi c, E. Mayerhofer, and J. Teichmann. Affi ne processes on positive semidefinite
matrices. Annals of Applied Probability, 21(2):397-463, 2011.
C. Cuchiero, M. Keller-Ressel, and J. Teichmann. Polynomial processes and their applications to
mathematical nance. Finance and Stochastics, 16(4):711-740, 2012.
C. Cuchiero, M. Larsson, and S. Svaluto-Ferro. Probability measure-valued polynomial di usions.
Preprint, available at arXiv:1807.03229, 2018.
C. Cuchiero and J. Teichmann. Generalized Feller processes and Markovian lifts of stochastic
Volterra processes: the a ffine case, Preprint, available at arXiv:1804.10450, 2018.
C. Cuchiero. Polynomial processes in stochastic portfolio theory. Stochastic processes and their
applications, Forthcoming, 2018.
D. Duffi e, D. Filipovi c, and W. Schachermayer. Affi ne processes and applications in nance.
Annals of Applied Probability, 13:984-1053, 2003.
O. El Euch, M. Fukasawa, and M. Rosenbaum. The microstructural foundations of leverage e ect
and rough volatility. Finance and Stochastics, 22(2):241{280, 2018.
O. El Euch and M. Rosenbaum. The characteristic function of rough Heston models. Mathematical
Finance, 2016.
A. Etheridge. An Introduction to Superprocesses. University lecture series. American Mathematical
Society Volume 20, 2000.
R. Fernholz. Stochastic Portfolio Theory. Applications of Mathematics. Springer-Verlag, New
York, 2002.
R. Fernholz and I. Karatzas. Stochastic portfolio theory: an overview. Handbook of numerical
analysis, 15:89-167, 2009
D. Filipovi c and M. Larsson. Polynomial di usions and applications in Finance. Finance and
Stochastics, 20(4):931-972, 2016.
P. Henry-Labord ere, N. Oudjane, X. Tan, N. Touzi, and X. Warin. Branching di usion representation
of semilinear PDEs and Monte Carlo approximation. Preprint available at arXiv:1603.01727,
2016.
