Search result: Catalogue data in Autumn Semester 2018

Mathematics Master Information
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
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Selection: Numerical Analysis
NumberTitleTypeECTSHoursLecturers
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 credits3V + 1UA. Jentzen, L. Yaroslavtseva
AbstractCourse 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.
ObjectiveThe 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.
ContentGeneration 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 notesLecture notes are available as a PDF file: see Learning materials.
LiteratureP. 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 / NoticePrerequisites:

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.
401-4785-00LMathematical and Computational Methods in PhotonicsW8 credits4GH. Ammari
AbstractThe 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
ObjectiveThe 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.
401-4357-68LOn Deep Artificial Neural Networks and Partial Differential Equations Information W4 credits2GA. Jentzen
AbstractIn 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).
ObjectiveThe aim of this course is to teach the students a decent knowledge on deep artificial neural networks and their approximation capacities.
ContentIn 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 notesLecture notes will be available as a PDF file.
LiteratureRelated 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 [Link].

* 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 [Link].

* Andrew R. Barron,
Universal approximation bounds for superpositions of a sigmoidal function.
IEEE Trans. Inform. Theory 39 (1993), no. 3, 930--945.
Prerequisites / NoticePrerequisites:
Analysis I and II, Elementary Probability Theory, and Measure Theory
401-4503-68LReading Course: Reduced Basis MethodsW4 credits2GR. Hiptmair
AbstractReduced 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.
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.
LiteratureMain 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 / NoticeThis 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
NumberTitleTypeECTSHoursLecturers
401-4607-68LTopics on the Gaussian Free FieldW4 credits2VW. Werner
AbstractWe will discuss various aspects and properties of the Gaussian Free Field.
Objective
ContentTopics discussed will include:
- Discrete and continuous Gaussian Free Field
- Local sets.
- Relation to loop-soups.
- Uniform spanning trees.
401-4611-68LRegularity StructuresW6 credits3VJ. Teichmann
AbstractWe 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.
Objective
401-4619-67LAdvanced Topics in Computational Statistics
Does not take place this semester.
W4 credits2VN. Meinshausen
AbstractThis lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling.
ObjectiveStudents learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes.
ContentThe 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 / NoticeWe assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics.
401-3628-14LBayesian Statistics
Does not take place this semester.
W4 credits2V
AbstractIntroduction 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.
ObjectiveStudents understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis.
ContentTopics 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 notesA script will be available in English.
LiteratureChristian 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 / NoticeFamiliarity 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.
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples 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.
ObjectiveParticipants 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.
ContentPrinciples 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.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe 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.
401-0649-00LApplied Statistical RegressionW5 credits2V + 1UM. Dettling
AbstractThis 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.
ObjectiveThe students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling.
ContentThe 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 notesA script will be available.
LiteratureFaraway (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 / NoticeThe 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.
401-4637-67LOn Hypothesis TestingW4 credits2VF. Balabdaoui
AbstractThis course is a review of the main results in decision theory.
ObjectiveThe 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)
401-3627-00LHigh-Dimensional Statistics
Does not take place this semester.
W4 credits2VP. 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.
ObjectiveKnowledge of methods and basic theory for high-dimensional statistical inference
ContentLasso 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
LiteraturePeter 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 / NoticeKnowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics).
401-4623-00LTime Series AnalysisW6 credits3GN. Meinshausen
AbstractStatistical 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.
ObjectiveUnderstanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
ContentThis 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 notesNot available
LiteratureA list of references will be distributed during the course.
Prerequisites / NoticeBasic knowledge in probability and statistics
401-3612-00LStochastic SimulationW5 credits3GF. Sigrist
AbstractThis 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.
ObjectiveStochastic 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.
ContentExamples 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 notesA script will be available in English.
LiteratureP. 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 / NoticeFamiliarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed.
401-3822-17LIsing Model and Its Geometric Representations Information W4 credits2VV. Tassion
Abstract
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 (Link) after having received the credits.
NumberTitleTypeECTSHoursLecturers
401-3925-00LNon-Life Insurance: Mathematics and Statistics Information W8 credits4V + 1UM. V. Wüthrich
AbstractThe 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.
ObjectiveThe 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.
ContentThe 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 notesM. V. Wüthrich, Non-Life Insurance: Mathematics & Statistics
Link
Prerequisites / NoticeThe 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 Link.

Prerequisites: knowledge of probability theory, statistics and applied stochastic processes.
401-3922-00LLife Insurance MathematicsW4 credits2VM. Koller
AbstractThe 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.
Objective
401-3928-00LReinsurance AnalyticsW4 credits2VP. Antal, P. Arbenz
AbstractThis 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
ObjectiveThis 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
ContentThis 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 notesSlides, lecture notes, and references to literature will be made available.
Prerequisites / NoticeBasic knowledge in statistics, probability theory, and actuarial techniques
401-3927-00LMathematical Modelling in Life InsuranceW4 credits2VT. J. Peter
AbstractIn 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.
ObjectiveThe 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.
ContentFollowing 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 notesLectures notes and slides will be provided
Prerequisites / NoticeThe 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.
401-4912-11LTrends in Stochastic Portfolio TheoryW4 credits2VM. Larsson
AbstractThis 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.
Objective
ContentThis 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 / NoticePrerequisites: 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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