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- Robust pricing, hedging and investing in discrete time | Applied Financial Mathematics

10623 Berlin 4 p m Ludovic Tangpi HU Berlin We provide a theoretical framework for pricing hedging and investing in a model independent financial market Our method relies on representation results for convex increasing functionals and extends to hedging problems with given marginals Based on joint works with P Cheridito and M Kupper News Computer klüger als der Mensch Das vergessene Werkzeug der Ökonomie Research Projects funded under HU s

Original URL path: http://horst.qfl-berlin.de/robust-pricing-hedging-and-investing-discrete-time (2016-04-24)

Open archived version from archive - Application of PPDEs to stochastic differential games | Applied Financial Mathematics

Search this site You are here Home Application of PPDEs to stochastic differential games Application of PPDEs to stochastic differential games 9 July 2015 Kategorie Research Seminars TU Berlin Room MA 041 Straße des 17 Juni 136 10623 Berlin 5 p m Ibrahim Ekren ETH Zürich In this talk we define derivatives of functionals on the space of continuous paths and give an introduction to path dependent partial differential equations PPDEs These equations extend the well known Feynman Kac Formula to a non Markovian framework Since the space of continuous paths is not locally compact we cannot rely on the theory of viscosity solutions for PDEs and need to develop new approaches We present new results on degenerate PPDEs and apply them to the study of non Markovian stochastic differential games This talk is based on joint works with Nizar Touzi and Jianfeng Zhang 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 both internships and permanent positions Please use the following Link if you

Original URL path: http://horst.qfl-berlin.de/application-ppdes-stochastic-differential-games (2016-04-24)

Open archived version from archive - Further Advances in Nonconventional Limit Theorems | Applied Financial Mathematics

136 10623 Berlin 6 p m Yuri Kifer Hebrew University Jerusalem Nonconventional limit theorems deal with the asymptotic behavior of sums of the form sum n 1 N F xi q 1 n xi q 2 n xi q l n where F is a function xi n n geq 0 is a stochastic process with some stationarity properties in particular it can be generated by a measure preserving transformation T in the form xi n f circ T n where f is a function The functions q j n j 1 l take on nonnegative integer values on nonnegative integers and they satisfy some properties for instance they may have the form q j n jn We discuss first the crucial question on positivity of the limiting variance for the sums above and then exhibit new results concerning the nonconventional local limit theorem Berry Esseen type estimates and the functional central limit theorem for the case when q j n s are general integer valued polynomials These results are obtained together with my student Yeor Hafouta News Computer klüger als der Mensch Das vergessene Werkzeug der Ökonomie Research Projects funded under HU s strategic partnership programs with Princeton University

Original URL path: http://horst.qfl-berlin.de/further-advances-nonconventional-limit-theorems (2016-04-24)

Open archived version from archive - Benchmarked Risk Minimization | Applied Financial Mathematics

of Technology Sydney The presentation discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark the numeraire portfolio as reference unit The proposed concept of benchmarked risk minimization generalizes classical risk minimization pioneered by Föllmer Sondermann and Schweizer The latter relies on a quadratic criterion requesting the square integrability of contingent claims and the existence of an equivalent risk neutral probability measure The proposed concept of benchmarked risk minimization avoids these restrictive assumptions It employs the real world probability measure as pricing measure and identifies the minimal possible price for the hedgeable part of a contingent claim Furthermore the resulting benchmarked profit and loss is only driven by nontraded uncertainty and forms a martingale that starts at zero Benchmarked profit and losses when pooled and sufficiently independent become in total negligible This property is highly desirable from a risk management point of view It is making asymptotically benchmarked risk minimization the least expensive method for pricing and hedging of an increasing number of not fully replicable benchmarked contingent claims This is a joint work with Ke Du News Computer klüger als der Mensch Das vergessene Werkzeug der Ökonomie Research Projects funded under HU s strategic partnership

Original URL path: http://horst.qfl-berlin.de/benchmarked-risk-minimization (2016-04-24)

Open archived version from archive - Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes | Applied Financial Mathematics

Research Seminars TU Berlin Room MA 041 Straße des 17 Juni 136 10623 Berlin 5 p m Laurent Denis University of Le Mans We present an approach to absolute continuity and regularity of laws of Poisson functionals based on the framework of local Dirichlet forms The method mainly uses the chaos decomposition of the Poisson L 2 space which extends naturally to a chaos decomposition of the domain of the candidate closed form and gives rise to a new explicit calculus it consists in adding a particle and taking it back after computing the gradient This method that we call the lent particle method permits to develop a Malliavin calculus on the Poisson space and to obtain in a simple way existence of density and regularity of laws of Poisson functionals This talk is devoted to the practice of the method first on some simple examples and then on more sophisticated ones This talk is based on several joint works with N Bouleau and is the subject of a book soon to be released 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

Original URL path: http://horst.qfl-berlin.de/dirichlet-forms-methods-poisson-point-measures-and-l%C3%A9vy-processes (2016-04-24)

Open archived version from archive - Rank-based Markov chains, self-organized criticality, and order book dynamics | Applied Financial Mathematics

TU Berlin Room MA 041 Straße des 17 Juni 136 10623 Berlin 6 p m Jan Swart Prag In this talk we will take a look at some systems of interacting particles on the real line where the only spatial structure that is relevant for the dynamics is the relative order of the particles Examples of such systems are the modified Bak Sneppen model introduced as a variation of the original 1993 model by Meester and Sarkar 2012 Barabási s 2005 queueing system and a variation on the latter due to Gabrielli and Caldarelli 2009 a model for the evolution of the state of an order book on a stock market introduced by Stigler 1964 and independently by Luckock 2003 and a two models for canyon formation introduced by me 2014 All these systems employ a version of the rule kill the lowest particle and seem to exhibit self organized criticality at a critical point that marks the boundary between an interval where all particles are eventually removed and an interval where particle stay in the system forever News Computer klüger als der Mensch Das vergessene Werkzeug der Ökonomie Research Projects funded under HU s strategic partnership programs with Princeton

Original URL path: http://horst.qfl-berlin.de/rank-based-markov-chains-self-organized-criticality-and-order-book-dynamics (2016-04-24)

Open archived version from archive - Incorporating parameter risk into derivatives prices - an approach to bid-ask spreads | Applied Financial Mathematics

parameter risk into derivatives prices an approach to bid ask spreads Incorporating parameter risk into derivatives prices an approach to bid ask spreads 11 June 2015 Kategorie Research Seminars TU Berlin Room MA 041 Straße des 17 Juni 136 10623 Berlin 4 p m Karl Bannör Deloitte Touche GmbH We present a new method based on convex risk measures to incorporate parameter risk e g estimation and calibration risk into derivative prices generalizing the well known conic finance approach In this context weak continuity properties of convex risk measures are discussed As an application we calculate parameter risk implied bid ask spreads of exotics enabling us to compare the parameter risk of different models and different exotics Furthermore we introduce a nonparametric calibration procedure to real world bid ask prices using distortion risk measures and obtain empirical results both in the conic finance framework as well as employing the new method 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 both internships and permanent positions

Original URL path: http://horst.qfl-berlin.de/incorporating-parameter-risk-derivatives-prices-approach-bid-ask-spreads (2016-04-24)

Open archived version from archive - Non-colliding Ornstein-Uhlenbeck bridges and symmetry breaking in a quantum 1D Coulomb system | Applied Financial Mathematics

1D Coulomb system Non colliding Ornstein Uhlenbeck bridges and symmetry breaking in a quantum 1D Coulomb system 3 June 2015 Kategorie Research Seminars TU Berlin Room MA 041 Straße des 17 Juni 136 10623 Berlin 6 p m Kolloquium Sabine Jansen Bochum Jellium is a model where negatively charged electrons move in a uniform neutralizing background of positive charge Eugene Wigner conjectured that at low density the electrons should crystallize i e form a periodic lattice We prove that in dimension 1 in a quantum mechanics setup this actually happens for all temperatures and densities thereby extending low density results by Brascamp and Lieb 1975 and classical results by Aizenman and Martin 1980 The proof uses the Feynman Kac formula to map the quantum model to asystem of non colliding Ornstein Uhlenbeck bridges and then applies the Krein Rutman theorem an infinite dimensional version of Perron Frobenius The talk is based on joint work with Paul Jung University of Alabama at Birmingham 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

Original URL path: http://horst.qfl-berlin.de/non-colliding-ornstein-uhlenbeck-bridges-and-symmetry-breaking-quantum-1d-coulomb-system-0 (2016-04-24)

Open archived version from archive