Christa Cuchiero

Signature methods represent a non-parametric way for extracting characteristic features from time series data which is essential in machine learning tasks, mathematical finance and risk assessment. Indeed, signature-based approaches allow for data-driven and thus more robust model selection mechanisms, while first principles like no arbitrage can still be easily guaranteed.

One focus of this talk lies on the use of signature as universal linear regression basis of certain continuous paths functionals in financial applications. In these applications key quantities that have to be computed efficiently are the expected signature or the characteristic function of the signature of some underlying stochastic process. Surprisingly this can be achieved for generic classes of diffusion processes, called signature SDEs, via techniques from affine and polynomial processes.

In terms of concrete applications, we present several recent contributions ranging from signature-based asset price models for joint VIX and SPX calibration, over control problems in stochastic portfolio theory to functional Taylor expansions of path-dependent options.

The talk is based on several joint works with Guido Gazzani, Xin Guo, Janka Möller, Francesca Primavera, Sara-Svaluto Ferro and Josef Teichmann.

Christa Cuchiero is a full professor at the University of Vienna. She earned her doctorate in Mathematics from ETH Zurich in 2011. Her research centers around mathematical finance, stochastic analysis, quantitative risk management and machine learning. She is particularly interested in classes of universal stochastic processes with applications in volatility modeling and portfolio theory, approximation theory in dynamic situations, data-driven risk inference and machine learning in finance. Christa Cuchiero has received several prizes and fellowships, including the prestigious START award of the Austrian Science Fund (FWF). She has given a number of keynote speeches and serves on the editorial board of several academic journals. She has also co-organized international conferences and a world online seminar series on machine learning in finance.