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- Minicourse on Random Interlacements | Applied Financial Mathematics

2007 This model has originally been motivated by questions about the disconnection of discrete cylinders and tori by the trace of simple random walk as well as by related problems that have been investigated in the theoretical physics literature Intuitively random interlacements is a random subset of Z d d 2 which appears as the limiting distribution of the trace of simple random walk on a large torus when it runs up to times proportional to the volume It serves as a model for corrosion and in addition gives rise to interesting and challenging percolation problems The principal result imposing the structure of these lectures is the non triviality of the percolation phase transition for the vacant set i e the complement of random interlacements We will start with giving a short review of basic potential theory and then motivate how the model appears as the limiting distribution of simple random walk on the torus Next to obtain a better feeling for random interlacements we will compare it to the well known model of Bernoulli percolation and in particular show that there is no domination of one of them by the other We will then focus on the strong correlations of the model and show how these can be dealt with by the use of so called decoupling inequalities These can then be employed in order to deduce the main result If time admits we will sketch some more recent developments and applications of random interlacements in particular with a view to the Gaussian free field 24 06 2014 16 15 17 45 room MA748 RTG Lounge TU Berlin 26 06 2014 10 15 11 45 room 1 023 BMS Lounge HU Berlin 27 06 2014 10 15 11 45 room MA748 RTG Lounge TU Berlin News Computer klüger als

Original URL path: http://horst.qfl-berlin.de/minicourse-random-interlacements (2016-04-24)

Open archived version from archive - Valuation in illiquid markets | Applied Financial Mathematics

instruments under these market conditions The classical valuation theory which is based on the law of one price assumes implicitly that market participants can trade freely in both directions at the same price In the absence of perfect liquidity the law of one price should be replaced by a two price theory where the terms of trade depend on the direction of the trade We develop here a static as well as a continuous time theory for two price economies The two prices are termed bid and ask or lower and upper price but they should not be confused with the vast literature relating bid ask spreads to transaction costs or other frictions involved in modeling fi nancial markets The bid price arises as the infimum of test valuations given by certain market scenarios whereas the ask price is the supremum of such valuations The two prices correspond to nonlinear expectation operators The approach is made operational by using probability as well as measure distortions We discuss in detail the validity of the Feynman Kac representation of solutions of partial integro di fferential equations on which the dynamic theory is based Specifi c models which are driven by purely discontinuous

Original URL path: http://horst.qfl-berlin.de/tba-7 (2016-04-24)

Open archived version from archive - Fundamental theorem of asset pricing without reference measure | Applied Financial Mathematics

theorem of asset pricing without reference measure 19 June 2014 Kategorie Research Seminars TU Berlin Room MA 041 Straße des 17 Juni 136 10623 Berlin 4 p m Ludovic Tangpi Universität Konstanz When a financial market is governed by a single probability measure the absence of arbitrage opportunities is characterized by the existence of equivalent martingale or local martingale measures In this talk we focus on the fundamental theorem of asset pricing in the case where the market is governed by a non dominated set of probability measures We introduce the concept of free lunch with disappearing risk Our main result shows that in a continuous time model if the agent is allowed to trade only with strategies that are simple integrands then the absence of such free lunches is equivalent to the existence of a set of local martingale measures equivalent to the set of possible models Talk based on a joint work with Michael Kupper and Patrick Cheridito News Computer klüger als der Mensch Das vergessene Werkzeug der Ökonomie Research Projects funded under HU s strategic partnership programs with Princeton University and NUS Young researcher worksho p d fine job opportunities d fine continuously offers job opportunities for

Original URL path: http://horst.qfl-berlin.de/fundamental-theorem-asset-pricing-without-reference-measure (2016-04-24)

Open archived version from archive - Master equation for mean-field games | Applied Financial Mathematics

games Master equation for mean fi eld games 11 June 2014 Kategorie Research Seminars WIAS Berlin Mohrenstraße 39 Erhard Schmidt Saal 6 p m François Delarue Université Nice Sophia Antipolis CNRS Mean fi eld games are part of large population stochastic control The point is to describe asymptotic Nash equilibria within a large asymptotically infi nite population of controlled players interacting one with another in a mean fi eld way The purpose of the talk is to make rigorous the notion of master equation The master equation is a PDE built on the space of measures It encapsulates all the necessary information to describe an equilibrium Part of talk will be dedicated to the construction of a solution based on the analysis of the flow of a suitable forward backward SDE system To conclude I will show how to use the master equation to justify the passage from a finite population to an infi nite one News Computer klüger als der Mensch Das vergessene Werkzeug der Ökonomie Research Projects funded under HU s strategic partnership programs with Princeton University and NUS Young researcher worksho p d fine job opportunities d fine continuously offers job opportunities for students and university graduates

Original URL path: http://horst.qfl-berlin.de/tba-3 (2016-04-24)

Open archived version from archive - Events | Applied Financial Mathematics

Humboldt Distinguished Lecture Series in Applied Mathematics RUD 25 Room 1 115 Lecturer Xunyu Zhou This lecture series is intended for graduate students in mathematics and economics This year it is given by a pioneer in stochastic optimization and renowned financial mathematician 11 April 2013 On arbitrages arising with honest times Lecturer Monique Jeanblanc http www qfl berlin com arbitrages arising honest times 11 April 2013 Dynamics of Contract Design with Screening Lecturer Jaksa Cvitanic http www qfl berlin com dynamics contract design screening 11 October 2012 13 October 2012 4th Berlin Workshop on Mathematical Finance for Young Researchers The 4th Berlin Workshop on Mathematical Finance for Young Researchers provides a forum for PhD students postdoctoral researchers and young faculty members from all over the world 25 April 2012 26 April 2012 4th Humboldt Distinguished Lecture Series in Applied Mathematics The Humboldt Distinguished Lecture Series in Applied Mathematics is intended for graduate students in mathematics and economics 28 October 2011 29 October 2011 3rd Humboldt Princeton Conference The 3rd Humboldt Prinecton Conference focusses on Risk Patterns in Economics Statistics Finance and Medicine It takes place 27 September 2011 7 October 2011 BMS Summer School Random Motions and Random Graphs The BMS Summer School 2011 will take place at TU from September 26 October 7 2011 The topic will be Random motions and random graphs http www math berlin de Summer School 12 April 2011 13 April 2011 Humboldt Distinguished Lecture Series in Applied Mathematics The 2011 Humboldt Distinguished Lecture Series in Applied Mathematics is given by Ivar Ekeland on Asymmetry of Information in Finance 23 June 2010 24 June 2010 Humboldt Distinguished Lecture Series in Applied Mathematics The 2010 Humboldt Distinguished Lecture Series in Applied Mathematics is given by Darrell Duffie Stanford University on Dark Markets The event takes place

Original URL path: http://horst.qfl-berlin.de/newsandevents?page=10 (2016-04-24)

Open archived version from archive - Estimate nothing | Applied Financial Mathematics

the econometrics of financial time series it is customary to take some parametric model for the data and then estimate the parameters from historical data This approach suffers from several problems Firstly how is estimation error to be quantified and then taken into account when making statements about the future behaviour of the observed time series Secondly decisions may be taken today committing to future actions over some quite long horizon as in the trading of derivatives if the model is re estimated at some intermediate time our earlier decisions would need to be revised but the derivative has already been traded at the earlier price Thirdly the exact form of the parametric model to be used is generally taken as given at the outset other competitor models might possibly work better in some circumstances but the methodology does not allow them to be factored into the inference What we propose here is a very simple Bayesian alternative approach to inference and action in financial econometrics which deals decisively with all these issues The key feature is that nothing is being estimated News Computer klüger als der Mensch Das vergessene Werkzeug der Ökonomie Research Projects funded under HU s strategic

Original URL path: http://horst.qfl-berlin.de/estimate-nothing (2016-04-24)

Open archived version from archive - Efficient Laplace and Fourier inversions and Wiener-Hopf factorization in financial applications | Applied Financial Mathematics

in financial applications Efficient Laplace and Fourier inversions and Wiener Hopf factorization in financial applications 5 June 2014 Kategorie Research Seminars TU Berlin Room MA 041 Straße des 17 Juni 136 10623 Berlin 5 p m Sergei Levendorskii Leicester University Appropriate conformal deformations increase the speed and accuracy of calculation of fairly complicated oscillatory integrals in option pricing formulas in many cases when standard approaches are either too slow or inaccurate or both When several Laplace and Fourier inversions are needed it is necessary to use a family of contour transformations more flexible than Talbot s deformation of the contour in the Bromwich integral Further step in a general program of study of the efficiency of combinations of one dimensional inverse transforms for high dimensional inversions Abate Whitt Abate Valko and others Among applications pricing European options in Lévy models Heston model and more general SV models pricing options with barrier and lookback features and CDS in Lévy models News Computer klüger als der Mensch Das vergessene Werkzeug der Ökonomie Research Projects funded under HU s strategic partnership programs with Princeton University and NUS Young researcher worksho p d fine job opportunities d fine continuously offers job opportunities for students

Original URL path: http://horst.qfl-berlin.de/tba-6 (2016-04-24)

Open archived version from archive - Interacting particle systems, nonlinear Markov processes and SDEs driven by nonlinear Levy noise | Applied Financial Mathematics

We shall discuss general approaches to the analysis of the dynamics of interacting particle systems their dynamic law of large numbers and the dynamic central limit for the fluctuations stressing both analytic aspects nonlinear Markov semigoups and processes and probablistic weak SDEs driven by nonlinear Levy noise Recent developments include the application to stochastic control e g mean field games with various applications in economics and finances News Computer klüger

Original URL path: http://horst.qfl-berlin.de/tba-5 (2016-04-24)

Open archived version from archive