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Вторая Летняя школа по финансовой математике 2015

28 июня - 4 июля 2015
Санкт-Петербург, г. Пушкин

Организатор: МЛКФ НИУ ВШЭ
Лекторы Школы
 
 
Rama Cont, Imperial Colledge, London, http://www.imperial.ac.uk/people/r.cont
Andreas Hamel,  Free University Bolzano-Bozen, http://www.salto.bz/article/14072014/burning-function
Mathieu Rosenbaum,  Université Pierre et Marie Curie, Paris, http://www.crest.fr/ses.php?user=3046
Nizar Touzi, Ecole Polytechnique, Paris, http://www.cmap.polytechnique.fr/~touzi/

Оргкомитет Школы
Юрий Кабанов, Михаил Житлухин, Алексей Муравлёв, Екатерина Паламарчук, Анастасия Элланская


Секретарь Школы
Георгий Шахназарянц gshahnazaryanc@hse.ru


Место проведения
Учебный центр подготовки руководителей (Санкт-Петербург, г. Пушкин)
Национальный исследовательский университет «Высшая школа экономики»

Темы курсов:


Andreas Hamel: Set-valued models in finance

 

Titles of  lectures (5 talks х 1 h 20 min):

1.1

Set-valued functions for market models with transaction costs: superhedging portfolios, risk measures, liquidation mappings.

1.2

An abstract framework for set-valued translative functions and their scalarizations.

1.3

Set-valued convex analysis and optimization.

1.4

Risk minimization/allocation and utility maximization for set-valued models in markets with transaction costs.

1.5

Auxiliary topics and open problems: stochastic dominance for multivariate random variables, set-valued V@R and AV@R, computational issues and more.  

Prerequisites:
1. General familiarity with (dual pairs of) locally convex spaces, Hahn-Banach/separation etc., see, e.g., chapters 5 and 7 of Aliprantis/Border, Infinite dimensional analysis, 3rd edition, 2006, as well as convex duality theory for scalar functions, see, e.g., Ekeland/Teman, Convex analysis and variational inequalities, SIAM 1999, chapters I-III.
2. General familiarity with market models with transaction costs as presented in Kabanov/Safarian, Markets with transaction costs, 2009.
3. A first read of Hamel et al., Set optimization - a rather short introductionhttp://arxiv.org/abs/1404.5928

Mathieu Rosenbaum: High frequency trading

 

Titles of lectures (5 talks х 1 h 20 min):

1.1

Introduction to high frequency modeling.

1.2

High frequency statistical estimation: Part 1.

1.3

High frequency statistical estimation: Part 2.

1.4

Around the tick size issue.

1.5

Volatility is rough.

 

Nizar Touzi: Martingale optimal transport

 

Titles of lectures (4 talks х 1 h 20 min):

1.1

Quick review on optimal transport.

1.2

Martingale optimal transport and robust hedging: formulation and duality.

1.3

Existence of semi-static hedging strategy.

1.4

Connection with the Skorohod embedding, and some continuous-time aspects.


 

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