Search result: Catalogue data in Autumn Semester 2018

Number	Title	Type	ECTS	Hours	Lecturers
Mathematics Master
Electives For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.
Electives: Applied Mathematics and Further Application-Oriented Fields ¬
Selection: Numerical Analysis
401-4657-00L	Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"	W	6 credits	3V + 1U	A. Jentzen, L. Yaroslavtseva
Abstract	Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
Learning objective	The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
Content	Generation of random numbers Monte Carlo methods for the numerical integration of random variables Stochastic processes and Brownian motion Stochastic ordinary differential equations (SODEs) Numerical approximations of SODEs Applications to computational finance: Option valuation
Lecture notes	Lecture notes are available as a PDF file: see Learning materials.
Literature	P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992.
Prerequisites / Notice	Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday, September 19, 2018. Date of the End-of-Semester examination: Wednesday, December 19, 2018, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19. Room for the End-of-Semester examination: ETH HG E 19. Exam inspection: Tuesday, February 26, 2019, 12:00-13:00 at HG D 7.2. Please bring your legi.
401-4785-00L	Mathematical and Computational Methods in Photonics	W	8 credits	4G	H. Ammari
Abstract	The aim of this course is to review new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods used to address challenging problems in nanophotonics. The emphasis will be on analyzing plasmon resonant nanoparticles, super-focusing & super-resolution of electromagnetic waves, photonic crystals, electromagnetic cloaking, metamaterials, and metasurfaces
Learning objective	The field of photonics encompasses the fundamental science of light propagation and interactions in complex structures, and its technological applications. The recent advances in nanoscience present great challenges for the applied and computational mathematics community. In nanophotonics, the aim is to control, manipulate, reshape, guide, and focus electromagnetic waves at nanometer length scales, beyond the resolution limit. In particular, one wants to break the resolution limit by reducing the focal spot and confine light to length scales that are significantly smaller than half the wavelength. Interactions between the field of photonics and mathematics has led to the emergence of a multitude of new and unique solutions in which today's conventional technologies are approaching their limits in terms of speed, capacity and accuracy. Light can be used for detection and measurement in a fast, sensitive and accurate manner, and thus photonics possesses a unique potential to revolutionize healthcare. Light-based technologies can be used effectively for the very early detection of diseases, with non-invasive imaging techniques or point-of-care applications. They are also instrumental in the analysis of processes at the molecular level, giving a greater understanding of the origin of diseases, and hence allowing prevention along with new treatments. Photonic technologies also play a major role in addressing the needs of our ageing society: from pace-makers to synthetic bones, and from endoscopes to the micro-cameras used in in-vivo processes. Furthermore, photonics are also used in advanced lighting technology, and in improving energy efficiency and quality. By using photonic media to control waves across a wide band of wavelengths, we have an unprecedented ability to fabricate new materials with specific microstructures. The main objective in this course is to report on the use of sophisticated mathematics in diffractive optics, plasmonics, super-resolution, photonic crystals, and metamaterials for electromagnetic invisibility and cloaking. The book merges highly nontrivial multi-mathematics in order to make a breakthrough in the field of mathematical modelling, imaging, and optimal design of optical nanodevices and nanostructures capable of light enhancement, and of the focusing and guiding of light at a subwavelength scale. We demonstrate the power of layer potential techniques in solving challenging problems in photonics, when they are combined with asymptotic analysis and the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. In this course we shall consider both analytical and computational matters in photonics. The issues we consider lead to the investigation of fundamental problems in various branches of mathematics. These include asymptotic analysis, spectral analysis, mathematical imaging, optimal design, stochastic modelling, and analysis of wave propagation phenomena. On the other hand, deriving mathematical foundations, and new and efficient computational frameworks and tools in photonics, requires a deep understanding of the different scales in the wave propagation problem, an accurate mathematical modelling of the nanodevices, and fine analysis of complex wave propagation phenomena. An emphasis is put on mathematically analyzing plasmon resonant nanoparticles, diffractive optics, photonic crystals, super-resolution, and metamaterials.
401-4357-68L	On Deep Artificial Neural Networks and Partial Differential Equations	W	4 credits	2G	A. Jentzen
Abstract	In this lecture we rigorously analyse approximation capacities of deep artificial neural networks and prove that deep artificial neural networks do overcome the curse of dimensionality in the numerical approximation of solutions of partial differential equations (PDEs).
Learning objective	The aim of this course is to teach the students a decent knowledge on deep artificial neural networks and their approximation capacities.
Content	In recent years deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for a series of computational problems ranging from computer vision, image classification, speech recognition, and natural language processing to computational advertisement. Such numerical simulations indicate that deep artificial neural networks seem to admit the fundamental power to overcome the curse of dimensionality when approximating the high-dimensional functions appearing in the above named applications. In this lecture we rigorously analyse approximation capacities of deep artificial neural networks and prove that deep artificial neural networks do overcome the curse of dimensionality in the numerical approximation of solutions of partial differential equations (PDEs). In particular, this course includes (i) a rigorous mathematical introduction to artificial neural networks, (ii) an introduction to some partial differential equations, and (iii) results on approximation capacities of deep artificial neural networks.
Lecture notes	Lecture notes will be available as a PDF file.
Literature	Related literature: * Arnulf Jentzen, Diyora Salimova, and Timo Welti, A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients. arXiv:1809.07321 (2018), 48 pages. Available online at [https://arxiv.org/abs/1809.07321]. * Philipp Grohs, Fabian Hornung, Arnulf Jentzen, and Philippe von Wurstemberger, A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. arXiv:1809.02362 (2018), 124 pages. Available online at [https://arxiv.org/abs/1809.02362]. * Andrew R. Barron, Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39 (1993), no. 3, 930--945.
Prerequisites / Notice	Prerequisites: Analysis I and II, Elementary Probability Theory, and Measure Theory
401-4503-68L	Reading Course: Reduced Basis Methods	W	4 credits	2G	R. Hiptmair
Abstract	Reduced Basis Methods (RBM) allow the efficient repeated numerical soluton of parameter depedent differential equations, which arise, e.g., in PDE-constrained optimization, optimal control, inverse problems, and uncertainty quantification. This course introduces the mathematical foundations of RBM and discusses algorithmic and implementation aspects.
Learning objective	* Knowledge about the main principles underlying RBMs * Familiarity with algorithms for the construction of reduced bases * Knowledge about the role of and techniques for a posteriori error estimation. * Familiarity with some applications of RBMs.
Literature	Main reference: Hesthaven, Jan S.; Rozza, Gianluigi; Stamm, Benjamin, Certified reduced basis methods for parametrized partial differential equations. SpringerBriefs in Mathematics, 2016 Supplementary reference: Quarteroni, Alfio; Manzoni, Andrea; Negri, Federico, Reduced basis methods for partial differential equations. An introduction. Unitext 92, Springer, Cham, 2016.
Prerequisites / Notice	This is a reading course, which will closely follow the book by J. Hesthaven, G. Rozza and B. Stamm. Participants are expected to study particular sections of the book every week, which will then be discussed during the course sessions.

Selection: Probability Theory, Statistics
Number	Title	Type	ECTS	Hours	Lecturers
401-4607-68L	Topics on the Gaussian Free Field	W	4 credits	2V	W. Werner
Abstract	We will discuss various aspects and properties of the Gaussian Free Field.
Learning objective
Content	Topics discussed will include: - Discrete and continuous Gaussian Free Field - Local sets. - Relation to loop-soups. - Uniform spanning trees.
401-4611-68L	Regularity Structures	W	6 credits	3V	J. Teichmann
Abstract	We develop the main tools of Martin Hairer's theory of regularity structures to solve singular stochastic partial differential equations in a pathwise way or addtionally by re-normalization techniques.
Learning objective
401-4619-67L	Advanced Topics in Computational Statistics Does not take place this semester.	W	4 credits	2V	N. Meinshausen
Abstract	This lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling.
Learning objective	Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes.
Content	The main focus will be on graphical models in various forms: Markov properties of undirected graphs; Belief propagation; Hidden Markov Models; Structure estimation and parameter estimation; inference for high-dimensional data; causal graphical models
Prerequisites / Notice	We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics.
401-3628-14L	Bayesian Statistics Does not take place this semester.	W	4 credits	2V
Abstract	Introduction to the Bayesian approach to statistics: Decision theory, prior distributions, hierarchical Bayes models, Bayesian tests and model selection, empirical Bayes, computational methods, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods.
Learning objective	Students understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis.
Content	Topics that we will discuss are: Difference between the frequentist and Bayesian approach (decision theory, principles), priors (conjugate priors, Jeffreys priors), tests and model selection (Bayes factors, hyper-g priors in regression),hierarchical models and empirical Bayes methods, computational methods (Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods)
Lecture notes	A script will be available in English.
Literature	Christian Robert, The Bayesian Choice, 2nd edition, Springer 2007. A. Gelman et al., Bayesian Data Analysis, 3rd edition, Chapman & Hall (2013). Additional references will be given in the course.
Prerequisites / Notice	Familiarity with basic concepts of frequentist statistics and with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed.
401-0625-01L	Applied Analysis of Variance and Experimental Design	W	5 credits	2V + 1U	L. Meier
Abstract	Principles of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
Learning objective	Participants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
Content	Principles of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
Literature	G. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / Notice	The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
401-0649-00L	Applied Statistical Regression	W	5 credits	2V + 1U	M. Dettling
Abstract	This course offers a practically oriented introduction into regression modeling methods. The basic concepts and some mathematical background are included, with the emphasis lying in learning "good practice" that can be applied in every student's own projects and daily work life. A special focus will be laid in the use of the statistical software package R for regression analysis.
Learning objective	The students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling.
Content	The course starts with the basics of linear modeling, and then proceeds to parameter estimation, tests, confidence intervals, residual analysis, model choice, and prediction. More rarely touched but practically relevant topics that will be covered include variable transformations, multicollinearity problems and model interpretation, as well as general modeling strategies. The last third of the course is dedicated to an introduction to generalized linear models: this includes the generalized additive model, logistic regression for binary response variables, binomial regression for grouped data and poisson regression for count data.
Lecture notes	A script will be available.
Literature	Faraway (2005): Linear Models with R Faraway (2006): Extending the Linear Model with R Draper & Smith (1998): Applied Regression Analysis Fox (2008): Applied Regression Analysis and GLMs Montgomery et al. (2006): Introduction to Linear Regression Analysis
Prerequisites / Notice	The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software package R, for which an introduction will be held. In the Mathematics Bachelor and Master programmes, the two course units 401-0649-00L "Applied Statistical Regression" and 401-3622-00L "Regression" are mutually exclusive. Registration for the examination of one of these two course units is only allowed if you have not registered for the examination of the other course unit.
401-4637-67L	On Hypothesis Testing	W	4 credits	2V	F. Balabdaoui
Abstract	This course is a review of the main results in decision theory.
Learning objective	The goal of this course is to present a review for the most fundamental results in statistical testing. This entails reviewing the Neyman-Pearson Lemma for simple hypotheses and the Karlin-Rubin Theorem for monotone likelihood ratio parametric families. The students will also encounter the important concept of p-values and their use in some multiple testing situations. Further methods for constructing tests will be also presented including likelihood ratio and chi-square tests. Some non-parametric tests will be reviewed such as the Kolmogorov goodness-of-fit test and the two sample Wilcoxon rank test. The most important theoretical results will reproved and also illustrated via different examples. Four sessions of exercises will be scheduled (the students will be handed in an exercise sheet a week before discussing solutions in class).
Literature	- Statistical Inference (Casella & Berger) - Testing Statistical Hypotheses (Lehmann and Romano)
401-3627-00L	High-Dimensional Statistics Does not take place this semester.	W	4 credits	2V	P. L. Bühlmann
Abstract	"High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed.
Learning objective	Knowledge of methods and basic theory for high-dimensional statistical inference
Content	Lasso and Group Lasso for high-dimensional linear and generalized linear models; Additive models and many smooth univariate functions; Non-convex loss functions and l1-regularization; Stability selection, multiple testing and construction of p-values; Undirected graphical modeling
Literature	Peter Bühlmann and Sara van de Geer (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Verlag. ISBN 978-3-642-20191-2.
Prerequisites / Notice	Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics).
401-4623-00L	Time Series Analysis	W	6 credits	3G	N. Meinshausen
Abstract	Statistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
Learning objective	Understanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
Content	This course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations. Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
Lecture notes	Not available
Literature	A list of references will be distributed during the course.
Prerequisites / Notice	Basic knowledge in probability and statistics
401-3612-00L	Stochastic Simulation	W	5 credits	3G	F. Sigrist
Abstract	This course provides an introduction to statistical Monte Carlo methods. This includes applications of simulations in various fields (Bayesian statistics, statistical mechanics, operations research, financial mathematics), algorithms for the generation of random variables (accept-reject, importance sampling), estimating the precision, variance reduction, introduction to Markov chain Monte Carlo.
Learning objective	Stochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can be approximated by averaging simulated values, and the central limit theorem gives an estimate of the error of this approximation. The course shows examples of the many applications of stochastic simulation and explains different algorithms used for simulation. These algorithms are illustrated with the statistical software R.
Content	Examples of simulations in different fields (computer science, statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (quantile transform, accept-reject, importance sampling), simulation of Gaussian processes and diffusions. The precision of simulations, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC).
Lecture notes	A script will be available in English.
Literature	P. Glasserman, Monte Carlo Methods in Financial Engineering. Springer 2004. B. D. Ripley. Stochastic Simulation. Wiley, 1987. Ch. Robert, G. Casella. Monte Carlo Statistical Methods. Springer 2004 (2nd edition).
Prerequisites / Notice	Familiarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed.
401-3822-17L	Ising Model and Its Geometric Representations	W	4 credits	2V	V. Tassion
Abstract
Learning objective
Prerequisites / Notice	- Probability Theory.

Selection: Financial and Insurance Mathematics In the Master's programmes in Mathematics resp. Applied Mathematics 401-3913-01L Mathematical Foundations for Finance is eligible as an elective course, but only if 401-3888-00L Introduction to Mathematical Finance isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat) after having received the credits.
Number	Title	Type	ECTS	Hours	Lecturers
401-3925-00L	Non-Life Insurance: Mathematics and Statistics	W	8 credits	4V + 1U	M. V. Wüthrich
Abstract	The lecture aims at providing a basis in non-life insurance mathematics which forms a core subject of actuarial sciences. It discusses collective risk modeling, individual claim size modeling, approximations for compound distributions, ruin theory, premium calculation principles, tariffication with generalized linear models, credibility theory, claims reserving and solvency.
Learning objective	The student is familiar with the basics in non-life insurance mathematics and statistics. This includes the basic mathematical models for insurance liability modeling, pricing concepts, stochastic claims reserving models and ruin and solvency considerations.
Content	The following topics are treated: Collective Risk Modeling Individual Claim Size Modeling Approximations for Compound Distributions Ruin Theory in Discrete Time Premium Calculation Principles Tariffication and Generalized Linear Models Bayesian Models and Credibility Theory Claims Reserving Solvency Considerations
Lecture notes	M. V. Wüthrich, Non-Life Insurance: Mathematics & Statistics http://ssrn.com/abstract=2319328
Prerequisites / Notice	The exams ONLY take place during the official ETH examination period. This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under www.actuaries.ch. Prerequisites: knowledge of probability theory, statistics and applied stochastic processes.
401-3922-00L	Life Insurance Mathematics	W	4 credits	2V	M. Koller
Abstract	The classical life insurance model is presented together with the important insurance types (insurance on one and two lives, term and endowment insurance and disability). Besides that the most important terms such as mathematical reserves are introduced and calculated. The profit and loss account and the balance sheet of a life insurance company is explained and illustrated.
Learning objective
401-3928-00L	Reinsurance Analytics	W	4 credits	2V	P. Antal, P. Arbenz
Abstract	This course provides an actuarial introduction to reinsurance. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical models for extreme events such as natural or man-made catastrophes. The lecture covers reinsurance contracts, Experience and Exposure pricing, natural catastrophe modelling, solvency regulation, and alternative risk transfer
Learning objective	This course provides an introduction to reinsurance from an actuarial point of view. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical approaches associated with low frequency high severity events such as natural or man-made catastrophes. Topics covered include: - Reinsurance Contracts and Markets: Different forms of reinsurance, their mathematical representation, history of reinsurance, and lines of business. - Experience Pricing: Modelling of low frequency high severity losses based on historical data, and analytical tools to describe and understand these models - Exposure Pricing: Loss modelling based on exposure or risk profile information, for both property and casualty risks - Natural Catastrophe Modelling: History, relevance, structure, and analytical tools used to model natural catastrophes in an insurance context - Solvency Regulation: Regulatory capital requirements in relation to risks, effects of reinsurance thereon, and differences between the Swiss Solvency Test and Solvency 2 - Alternative Risk Transfer: Alternatives to traditional reinsurance such as insurance linked securities and catastrophe bonds
Content	This course provides an introduction to reinsurance from an actuarial point of view. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical approaches associated with low frequency high severity events such as natural or man-made catastrophes. Topics covered include: - Reinsurance Contracts and Markets: Different forms of reinsurance, their mathematical representation, history of reinsurance, and lines of business. - Experience Pricing: Modelling of low frequency high severity losses based on historical data, and analytical tools to describe and understand these models - Exposure Pricing: Loss modelling based on exposure or risk profile information, for both property and casualty risks - Natural Catastrophe Modelling: History, relevance, structure, and analytical tools used to model natural catastrophes in an insurance context - Solvency Regulation: Regulatory capital requirements in relation to risks, effects of reinsurance thereon, and differences between the Swiss Solvency Test and Solvency 2 - Alternative Risk Transfer: Alternatives to traditional reinsurance such as insurance linked securities and catastrophe bonds
Lecture notes	Slides, lecture notes, and references to literature will be made available.
Prerequisites / Notice	Basic knowledge in statistics, probability theory, and actuarial techniques
401-3927-00L	Mathematical Modelling in Life Insurance	W	4 credits	2V	T. J. Peter
Abstract	In Life insurance, it is essential to have adequate mortality tables, be it for reserving or pricing purposes. We learn to create mortality tables from scratch. Additionally, we study various guarantees embedded in life insurace products and learn to price them with the help of stochastic models.
Learning objective	The course's objective is to provide the students with the understanding and the tools to create mortality tables on their own. Additionally, students should learn to price embedded options in Life insurance. Aside of the mere application of specific models, they should develop an intuition for the various drivers of the value of these options.
Content	Following main topics are covered: 1. Overview on guarantees & options in life insurance with a real-world example demonstrating their risks 2. Mortality tables - Determining raw mortality rates - Smoothing of raw mortality rates - Trends in mortality rates - Lee-Carter model - Integration of safety margins 3. Primer on Financial Mathematics - Ito integral - Black-Scholes and Hull-White model 4. Valuation of Unit linked contracts with embedded options 5. Valuation of Participating contracts
Lecture notes	Lectures notes and slides will be provided
Prerequisites / Notice	The exams ONLY take place during the official ETH examination period. The course counts towards the diploma of "Aktuar SAV". Good knowledge in probability theory and stochastic processes is assumed. Some knowledge in financial mathematics is useful.
401-4912-11L	Trends in Stochastic Portfolio Theory	W	4 credits	2V	M. Larsson
Abstract	This course presents an introduction to Stochastic Portfolio Theory, which provides a mathematical framework for studying and exploiting empirically observed regularities of large equity markets. A central goal of the theory is to describe certain forms of arbitrage that arise over sufficiently long time horizons.
Learning objective
Content	This course presents an introduction to Stochastic Portfolio Theory, which provides a mathematical framework for studying and exploiting empirically observed regularities of large equity markets. A central goal of the theory is to describe certain forms of arbitrage that arise over sufficiently long time horizons. Since it was first introduced by Robert Fernholz almost 20 years ago, the theory has experienced rapid developments. This course will cover the foundations of Stochastic Portfolio Theory, including topics like relative arbitrage, functional portfolio generation, and capital distribution curves, as well as more recent developments.
Prerequisites / Notice	Prerequisites: Familiarity with Ito calculus at the level of Brownian Motion and Stochastic Calculus. Some background in mathematical finance is helpful. A course with similar content was offered in HS 2015 under the title "New Trends in Stochastic Portfolio Theory".

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