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Probability and Computational Finance Seminar
Christa Cuchiero
University of Vienna
Title: High and Infinite Dimensional Finance in the Light of Affine and Polynomial Processes

Abstract: A large part of quantitative questions in modern finance is concerned with high dimensionality, resulting from a great number of financial instruments, high frequency data and Non-Markovanity in certain financial time series. It raises issues on modeling, calibration and statistical estimation, and leads to high dimensional equations requiring efficient numerical tools and algorithms.

For tackling these kinds of problems we propose to use tractable infinite dimensional processes instead of relying on often highly stylized low dimensional factor models. The motivation for this approach is twofold: first, modeling high or even potentially infinite dimensional financial markets in a tractable and robust way, and second analyzing stochastic Volterra processes, which recently gained popularity through rough volatility models and ambit processes.

Both questions naturally lead to infinite dimensional affine and polynomial processes taking values in certain spaces of functions or measures. On the one hand, inspired from market weights modeling, we consider the space of probability measures on locally compact Polish space, where we can characterize polynomial diffusions, of which the well-known Fleming-Viot process is a specific example. On the other hand, we analyze infinite dimensional Markovian lifts of Volterra processes taking values in spaces of certain "forward curves" and show how -- in the case of affine or polynomial characteristics -- well-know properties transfer to the Volterra world.

Date: Monday, January 29, 2018
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Steve Shreve