Department of Mathematics and Systems Analysis
The talks are held in lecture hall U3 at Aalto University, Otakaari 1.

10.15-11.00 Gionis
11.15-12.00 Viitasaari
12.00-13.15 Lunch
13.30-14.15 Bauerschmidt
14.30-15-15 Pakkanen
15.15-15.45 Coffee
15.45-16.30 Peltola
The sauna is from 17.00 to 20.00 at Radisson Blu Hotel, Otaranta 2.

Titles and abstracts of the talks

"Eigenvectors and spectral measure of random regular graphs of fixed degree"
Roland Bauerschmidt (University of Cambridge)

I will discuss results on the delocalisation of eigenvectors and the spectral measure of random regular graphs with large but fixed degree. Our approach combines the almost deterministic structure of random regular graphs at small distances with random matrix like behaviour at large distances. This is joint work with Jiaoyang Huang and Horng-Tzer Yau.

"Mining temporal networks"
Aristides Gionis (Aalto University)

Large networks are being generated by applications that keep track of relationships between different data entities. Examples include online social networks recording interactions between individuals, sensor networks logging information exchanges between sensors, and more. There is a large body of literature on mining large networks, but most existing methods assume either static networks, or dynamic networks where the network topology is changing. On the other hand, in many real-world applications a continuous stream of interactions takes place on top of a relatively stable network topology, giving rise to different semantics than those of dynamic networks. In this talk we discuss two different problems that consider networks as a stream of interactions (edges) over time. In particular, we consider the problems of maintaining neighborhood profiles and tracking important nodes.For the studied problems we present new algorithms, and discuss our analytical results. We also present experimental evaluation on real-world datasets and case studies on different application scenarios.

"Rough volatility: towards efficient Monte Carlo pricing and calibration"
Mikko Pakkanen (Imperial College London)

Rough volatility is a new approach to the stochastic modelling of asset prices in continuous time, characterised by the use of stochastic processes rougher than Brownian motion to represent the time-varying magnitude (that is, volatility) of price fluctuations. As demonstrated by Gatheral, Jaisson, and Rosenbaum (2014) and Bayer, Friz, and Gatheral (2016), the rough volatility framework is remarkably consistent with both the time series properties of volatility and stylised facts of option prices (implied volatilities) across asset classes. Applying rough volatility models in option pricing is still not straightforward, however, as these models are necessarily non-Markovian and typically also non-affine, rendering conventional pricing methods such as partial differential equations and Fourier transforms inapplicable. In this talk, I outline some recent advances in simulation methodology for rough volatility models, which lead to a dramatic speed-up in Monte Carlo pricing. In particular, full calibration of rough volatility models to implied volatility surfaces is now within the realms of possibility. Joint work with Ryan McCrickerd.

"Multiple SLEs for \kappa \leq 4"
Eveliina Peltola (University of Geneva)

We discuss conformally invariant measures on families of curves known as multiple Schramm-Loewner evolutions (SLE_\kappa), that naturally correspond to interfaces in critical planar lattice models with alternating boundary conditions (”generalized Dobrushin boundary conditions”). When \kappa \leq 4, we can explicitly construct such multiple SLE measures using the Brownian loop measure. By a Markov chain argument, we can show that the multiple SLEs are uniquely characterized by a natural cascade property.

The talk is based on joint works with Hao Wu (Yau Mathematical Sciences Center / Tsinghua University) and Vincent Beffara (Université Grenoble Alpes, Institut Fourier).

"On model fitting and estimation of stationary processes"
Lauri Viitasaari (University of Helsinki)

Stationary processes form an important class of stochastic processes that has been extensively studied in the literature. Their applications include modelling and forecasting numerous real life phenomenon including natural disasters, sustainable energy sources, sales and market movements.
One of the most essential families of stationary processes is the ARMA family. When modelling existing data with ARMA process, the first step is to fix the orders of the model. After that, one can estimate the related parameters by using standard methods such as maximum likelihood (ML) or least squares (LS) estimators. The final step is to conduct various diagnostic tests in order to determine the quality of the model.
In this talk we present a novel way of fitting a model to a data that is assumed to be a realization from a discrete time stationary process. Our approach is based on a recently proved  AR(1) characterisation of stationary processes, where the noise is not assumed to be white. As a result, we obtain more general and easier way to fit a model into a stationary time series, thus outperforming traditional ARMA approaches. In particular, we obtain closed form consistent estimators of various model parameters and their asymptotic normality under general conditions. We also discuss continuous time extensions and application to the ARCH model with a memory effect.

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