Abstracts
Introduction to Traded Risk modeling framework
Marcin Pitera, Jagiellonian University Cracow
During this short course we will discuss selected aspects of Traded Risk modelling framework with focus put on its practical side. We will provide an overview of market risk models for which Internal Model Approach (IMA) could be used and discuss related mathematical concepts. This includes classical VaR, Stressed VaR, RNIV, IRC, as well as models related to FRTB regulatory update that are based on Expected Shortfall. Typical practical modelling approaches will be presented with detailed discussion of the underlying mathematical assumptions, limitations, and challenges. We will also outline the regulatory landscape and discuss standard model monitoring procedures. In particular, we will show how to assess VaR/ES model predictive accuracy and robustness via various backtesting procedures.
Stochastic-based approach in the industry applications
Agnieszka Wylomanska, Wroclaw University of Science and Technology
During the course students will have the opportunity to explore modern stochastic and time series modelling. First the classical time series models will be reminded, then the extensions of known systems will be presented. There will be classical autoregressive moving-average (ARMA) and priodic ARMA (PARMA) time series with Gaussian distribution. However because the Gaussian-based models are inappropriate for many real phenomena, the non-Gaussian systems will be introduced. The special attention will be paid to models based on the heavy-tailed (especially stable) distributions. The heavy-tailed distributions have found many practical applications and latest methods based on heavy-tailed distribution for the rigor analysis will be discussed. The estimation and simulation methods for time series models will be introduced. The students will have the opportunity to check those methods by using MATLAB codes. Moreover, the real industrial applications will be presented and the estimation and simulation methods will be used for real phenomena. The novelty of the course is lying on the combination of different techniques used in real data modelling. The real industrial phenomena applications can raise the interest of participants in the area of such effective mathematical models.
Lecture no. 1. "On various aspects of probability leading to new ways of processing information" (delivered on Monday, February 25th, 2019) (lecture notes 1, lecture notes 2)
Abstract: About complex numbers, called probability amplitudes, that,
unlike probabilities, can cancel each other out, leading to quantum
interference and qualitatively new ways of processing information.
Lecture no. 2 "Quantum entanglement" (lecture notes)
Abstract: About quantum entanglement, which has been singled out by
Erwin Schrödinger as ``...the characteristic trait of quantum
mechanics, the one that enforces its entire departure from classical
lines of thought.". Indeed, after playing a significant role in the
development of the foundations of quantum mechanics, quantum
entanglement became a new physical resource with potential commercial
applications. I will outline the evolution of the concept from its
origin, in around 1932, till today and describe some of its current
applications.