Beatrice Acciaio: Katalogdaten im Frühjahrssemester 2023

NameFrau Prof. Dr. Beatrice Acciaio
LehrgebietMathematik
Adresse
Professur für Mathematik
ETH Zürich, HG G 54.3
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 632 29 55
E-Mailbeatrice.acciaio@math.ethz.ch
URLhttps://people.math.ethz.ch/~beacciaio/
DepartementMathematik
BeziehungOrdentliche Professorin

NummerTitelECTSUmfangDozierende
401-0604-00LWahrscheinlichkeitstheorie und Statistik Information Belegung eingeschränkt - Details anzeigen 4 KP2V + 1UB. Acciaio
KurzbeschreibungWahrscheinlichkeitsmodelle und Anwendungen, Einführung in die Estimationstheorie und in die statistischen Tests.
LernzielFähigkeit, die behandelten wahrscheinlichkeitstheoretischen Methoden und Modellen zu verstehen und anzuwenden. Fähigkeit, einfache statistische Tests selbst durchzuführen und die Resultate zu interpretieren
InhaltDer Begriff Wahrscheinlichkeitsraum und einige klassische Modelle: Die Axiome von Kolmogorov, einfache Folgerungen, diskrete Modelle, Dichtefunktionen, Produktmodelle, Zusammenhang zwischen den bisher betrachteten Modellen, Verteilungsfunktionen, Transformation von Wahrscheinlichkeitsverteilungen. Bedingte Wahrscheinlichkeiten: Definition und Beispiele, Berechnung von absoluten aus bedingten Wahrscheinlichkeiten, Bayes'sche Regel, Anwendung auf Nachrichtenquellen, bedingte Verteilungen. Der Erwartungswert einer Zufallsvariablen, Varianz, Kovarianz und Korrelation, lineare Prognosen, das Gesetz der grossen Zahlen, der zentrale Grenzwertsatz. Einführung in die Statistik: Schätzung von Parametern, Tests.
Skriptja
LiteraturTextbuch: P. Brémaud: 'An Introduction to Probabilistic Modeling', Springer, 1988.
401-4498-DRLAdvances in Optimal Transport and Stochastics Belegung eingeschränkt - Details anzeigen
Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“.
1 KP2VG. Pammer, B. Acciaio
KurzbeschreibungWe study recent developments of stochastic transport with applications to mathematical finance. In particular, we will cover weak transport, martingale transport, causal and adapted transport.
LernzielUnderstanding of the main results and tools from classical transport and from the different new kinds of transports; intuition behind the main concepts and understanding of the proofs of the main results; ability to apply tools from optimal transport for applications in mathematical finance.
InhaltWe start by recalling the main concepts and results from the classical optimal transport theory, providing intuition of the main ideas and understanding of the needed mathematical methods. We then focus on recent developments of stochastic transport with applications to mathematical finance. In particular, we will cover the following topics: weak transport (including the special cases of entropic transport and barycentric transport), martingale transport (especially in connection with model-independent finance and the Skorokhod Embedding problem), causal and adapted transport (also related to stability in mathematical finance, and with applications to filtration enlargement, equilibrium problems, quantification of arbitrage). We will motivate the introduction of these different kinds of optimal transport in order to deal with several problems especially in mathematical finance, as pricing and hedging in a model-independent framework, gauging the distance between financial models, accounting for model uncertainty.
Skriptlecture notes will be provided at the beginning of the semester
Voraussetzungen / BesonderesMeasure Theory, Probability and Stochastic Calculus (basic)
401-4498-23LAdvances in Optimal Transport and Stochastics4 KP2VG. Pammer, B. Acciaio
KurzbeschreibungWe study recent developments of stochastic transport with applications to mathematical finance. In particular, we will cover weak transport, martingale transport, causal and adapted transport.
LernzielUnderstanding of the main results and tools from classical transport and from the different new kinds of transports; intuition behind the main concepts and understanding of the proofs of the main results; ability to apply tools from optimal transport for applications in mathematical finance.
InhaltWe start by recalling the main concepts and results from the classical optimal transport theory, providing intuition of the main ideas and understanding of the needed mathematical methods. We then focus on recent developments of stochastic transport with applications to mathematical finance. In particular, we will cover the following topics: weak transport (including the special cases of entropic transport and barycentric transport), martingale transport (especially in connection with model-independent finance and the Skorokhod Embedding problem), causal and adapted transport (also related to stability in mathematical finance, and with applications to filtration enlargement, equilibrium problems, quantification of arbitrage). We will motivate the introduction of these different kinds of optimal transport in order to deal with several problems especially in mathematical finance, as pricing and hedging in a model-independent framework, gauging the distance between financial models, accounting for model uncertainty.
SkriptLecture notes will be provided at the beginning of the semester
Voraussetzungen / BesonderesMeasure Theory, Probability and Stochastic Calculus (basic)
401-5910-00LTalks in Financial and Insurance Mathematics Information 0 KP1KB. Acciaio, P. Cheridito, D. Possamaï, M. Schweizer, J. Teichmann, M. V. Wüthrich
KurzbeschreibungForschungskolloquium
LernzielEinfuehrung in aktuelle Forschungsthemen aus dem Bereich "Insurance Mathematics and Stochastic Finance".
Inhalthttps://www.math.ethz.ch/imsf/courses/talks-in-imsf.html