How To Understand And Understand The Theory Of Computational Finance

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1 This course consists of three separate modules. Coordinator: Omiros Papaspiliopoulos Module I: Machine Learning in Finance Lecturer: Argimiro Arratia, Universitat Politecnica de Catalunya and BGSE Overview and Objectives Computational finance is a cross-disciplinary field which relies on computational intelligence, mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions. By employing various computational methods, practitioners of computational finance aim to forecast financial markets, assess the financial risk of various financial instruments, design strategies of investment. This course will give an introduction to Computational Finance focusing on the more computational aspects: machine learning-based financial models, optimization heuristics, online programming. Prerequisites Statistical Modelling and Inference Machine Learning Financial Econometrics Course Outline Nonlinear Time Series Models in Finance After a quick review of ARCH and GARCH models, we will study Neural Networks, Support Vector Machines and Kernel methods in financial forecasting and price modeling. 1

2 Optimization Heuristics in Finance Simulated Annealing, Genetic programming, Ant Colony optimization, and other heuristics and their application to parameter estimation of GARCH, automatic finding trading rules, valuing options. Online finance After a quick review of the principles of Markowitz mean-variance portfolio model, we pass on to study Cover s Universal portfolio framed in the theory of online problems and competitive analysis. Online portfolio selection. Required Activities Standard attendance to theory class and problem sets (that may include theory problems as well as practice with software and data sets). Evaluation Problem sets and a project covering topics and methodologies (models, algorithms,...) from the course. Materials Books: A. Arratia, Computational Finance, An Introductory Course with R, Atlantis Press & Springer, R. Tsay. Analysis of Financial Time Series. Wiley, 2013 McNelis, P. D. (2005). Neural Networks in Finance: Gaining predictive edge in the market. Elsevier Vapnik, V. N. (2000). The nature of statistical learning theory (2nd ed.). New York: Springer Borodin, A., & El-Yaniv, R. (1998). Online computation and competitive analysis. Cambridge University Press Cesa-Bianchi, N., & Lugosi, G. (2006). Prediction, learning, and games. Cambridge University Press. Other: A list of other resources (data sets, papers,... ) will be provided as the course progresses. 2

3 Module II: Recommender Systems Lecturer: Alexandros Karatzoglou, Telefonica and BGSE Overview and Objectives Recommender Systems are a vital component in many e-commerce sites (e.g. Amazon) and music or movies streaming services such as Netflix and Spotify. Most Recommender Systems are based on Machine Learning techniques that use the data-logs of the services and sites to discover patterns in the collective preferences of users. In this course we will delve into a number of these Machine Learning techniques that are used in Recommender Systems including factor models, memory-based methods and deep learning techniques. Prerequisites Basic Linear Algebra Machine Learning Course Outline Introduction to Recommender Systems We will have a quick look at the basic principles and ideas behind most modern recommender systems. Content-based Recommendation Principles of Content-based Recommendation, tf-idf, item-content similarities, user-content models Collaborative Filtering Memory-based methods, Clustering, Matrix Factorization, Restricted-Boltzmann Machines 3

4 Hybrid Recommenders and post-filtering Combining Collaborative and Content-based methods, Diversification Required Activities Standard attendance to theory class and problem sets (that will include practice with software and data sets). Evaluation Problem sets and a project covering topics and methodologies (models, algorithms,...) from the course. Materials Books: Recommender Systems Handbook, 2010 Francesco Ricci, Lior Rokachm Bracha Shapira Collaborative Filtering Recommender Systems, 2011, Michael Ekstrand, John Riedl, Joseph A. Konstan Programming Collective Intelligence: Building Smart Web 2.0 Applications, Toby Segaran 4

5 Module III: Topological Data Analysis Lecturer: Matthew Eric Bassett, Gower Street Analytics and BGSE Overview and Objectives Topological Data Analysis leverages mathematical topology to provide qualitative descriptions of high dimensional datasets, especially when the datasets come with niether a natural coordinate system nor a metric, and has found applications in neuroscience, fluid dynamics, genomics, et cetera. This module will introduce the topological concepts useful for dealing with high dimensional datasets: simplicial complexes, functoriality, and persistent homology, and show how these concepts can extract relevant features from their samples. The goal is to provide students with a firm scientific understanding of the methods in this area of research, while also understanding examples where these methods have seen success. This module will be theoretical and will only briefly cover applications or computational strategies. Prerequisites Basic Linear Algebra Multivariate Calculus Course Outline Basic Philosophy of TDA We will begin by explaining why Topology might have some use for data analysis. Point Clouds and Topological Coverings We will discuss methods for topologizing data by turning the underlying data set into a Simplicial Complex. 5

6 Invariants, Persistence, and what they mean for data Topological invariants, homology, Betti numbers, and their geometric and data analytic meaning. Manifold-Inspired methods Hodge Theory (Differential geometry) for Statistical Ranking, Discrete Calculus, Manifold learning. Required Activities Standard attendance to theory class and problem sets (that will include practice with software and data sets). Evaluation Problem sets and a project covering topics and methodologies (models, algorithms,...) from the course. Materials Papers: G. Carlsson, Topology and Data, Bulletin of the American Mathematical Society, v. 46 (2), 2009, pp R. Ghrist, Barcodes: The Persistent Topology of Data, Bulletin of the American Mathematical Society, v. 45 (1), 2008, pp X Jiang, L Lim, Y Yao, Y. Ye, Statistical Ranking and combinatorial Hodge theory, Mathematical Programming, v 127 (1) G Singh, et al, Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition, Eurographics Symposium on Point-Based Graphics,