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- Convergence and regularity of probability laws by using an interpolation method | Applied Financial Mathematics

by using an interpolation method 25 November 2015 Kategorie Research Seminars WIAS Erhard Schmidt Saal Mohrenstraße 39 10117 Berlin 6 p m Vlad Bally Marne la Vallée Fournier and Printems Bernoulli 2010 have recently established a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with Hölder continuous coefficients This is of course out of reach by using already classical probabilistic methods based on Malliavin calculus By employing some Besov space techniques Debussche and Romito Probab Theory Related Fields 2014 have substantially improved the result of Fournier and Printems In our paper we show that this kind of problem naturally fits in the framework of interpolation spaces we prove an interpolation inequality which allows to state and even to slightly improve the above absolute continuity result Moreover it turns out that the above interpolation inequality has applications in a completely different framework we use it in order to estimate the error in total variance distance in some convergence theorems 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

Original URL path: http://horst.qfl-berlin.de/convergence-and-regularity-probability-laws-using-interpolation-method (2016-04-24)

Open archived version from archive - On optimal transport under the causality constraint | Applied Financial Mathematics

here Home On optimal transport under the causality constraint On optimal transport under the causality constraint 19 November 2015 Kategorie Research Seminars Rudower Chaussee 25 Room 1 115 4 p m Julio Backhoff Universität Wien In this talk we shall examine causal transports and the associated optimal transportation problem under the causality constraint Pc introduced by Rémi Lasalle Loosely speaking causal transports are a relaxation of adapted processes in the same sense as Kantorovich transport plans are the extension of Monge type transport maps We will establish a simple primal dual picture of both Pc and the so called bicausal transportation problem whereby causality runs in both directions in euclidean space or equiv for discrete time processes Together with this we provide a dynamic programming principle which allows us to identify optimal bi causal transports under given conditions If time permits potential applications of the theory will be presented 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

Original URL path: http://horst.qfl-berlin.de/optimal-transport-under-causality-constraint (2016-04-24)

Open archived version from archive - Optimal market making | Applied Financial Mathematics

Olivier Guéant ENSAE ParisTech Market makers provide liquidity to other market participants they propose prices at which they stand ready to buy and sell a wide variety of assets Market makers face a complex dynamical optimization problem They need to propose bid and offer ask prices in an optimal way for making money out of the difference between these two prices their bid ask spread while mitigating the risk associated with price changes In practice market makers indeed seldom buy and sell simultaneously Therefore they hold long or short inventories and are exposed to market risk In my talk i I reconcile the different modelling approaches proposed in the literature since the publication of the seminal paper High frequency trading in a limit order book by Marco Avellaneda and Sasha Stoikov ii I prove new general results on the existence and the characterization of optimal market making strategies iii I obtain new closed form and almost closed form approximations for the optimal quotes and iv I discuss multi asset market making 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

Original URL path: http://horst.qfl-berlin.de/optimal-market-making (2016-04-24)

Open archived version from archive - Robustness of spatialpreferentialattachment networks | Applied Financial Mathematics

Erhard Schmidt Saal Mohrenstraße 39 10117 Berlin 6 p m Peter Mörters Bath A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrarily small positive retention probability We study robustness for graphs in which new vertices are given a spatial position on the unit circle and are connected to existing vertices with a probability favouring short spatial distances and high degrees In this model of a scale free network with clustering we can independently tune the power law exponent tau of the degree istribution and the exponent delta at which the connection probability decreases with the distance of two vertices We show that the network is robust if tau 2 1 delta but fails to be robust if tau 2 1 delta 1 This is the first instance of a scale free network where robustness depends not only on its degree distribution but also on its clustering features This is joint work with Emmanuel Jacob ENS Lyon 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

Original URL path: http://horst.qfl-berlin.de/robustness-spatialpreferentialattachment-networks (2016-04-24)

Open archived version from archive - Probability and Other Branches of Mathematics | Applied Financial Mathematics

Juni 136 10623 Berlin 6 p m Jordan Stoyanov Newcastle University This lecture will be addressed to a wide audience from undergraduate and graduate students in Mathematics Statistics Physics and Computer Science to MSc and PhD students in these areas and even to professionals It will be shown that diverse and intriguing problems from branches of Mathematics such as Analysis Combinatorics Theory of Functions Number Theory can be solved elegantly by using ideas and techniques from Probability It is remarkable that sometime these are the only available solutions A few of the topics listed below will be discussed in detail Combinatorial and algebraic identities Casino numbers They are infinitely many Bernoulli LLN and Weierstrass theorem by Bernstein polynomials Old UspenskyoeNß problem and its far extensions Buridan Donkey story Random walk in random environment Many ways to interpret and solve the equation X Y XY Values of the Riemann zeta functions via Cauchy distribution Probability in other areas of Mathematics a few exercises one open problem Questions comments suggestions from the audience during the lecture are very welcome 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/probability-and-other-branches-mathematics (2016-04-24)

Open archived version from archive - The Emergence of Delta-Vega Hedging in the Black-Scholes Model | Applied Financial Mathematics

option pricing and hedging with uncertainty about a Black Scholes reference model For dynamic trading in the underlying asset and a liquidly traded vanilla option delta vega hedging is asymptotically optimal in the limit for small uncertainty aversion The corresponding price corrections are determined by a number of second order greeks namely the option s gamma vanna and volga Joint work with Sebastian Herrmann News Computer klüger als der Mensch

Original URL path: http://horst.qfl-berlin.de/emergence-delta-vega-hedging-black-scholes-model (2016-04-24)

Open archived version from archive - Paracontrolled KPZ equation | Applied Financial Mathematics

equation using paracontrolled distributions For example we will see that the solution to KPZ is given by the value function of an optimal control problem where a Brownian motion is steered through a white noise potential We will also study discretizations la Sasamoto Spohn and prove their convergence to the KPZ equation or a modified version of it This is joint work with Massimiliano Gubinelli News Computer klüger als der

Original URL path: http://horst.qfl-berlin.de/paracontrolled-kpz-equation (2016-04-24)

Open archived version from archive - Stochastic dynamics near a change of stability (Amplitude- and Modulation-Equations) | Applied Financial Mathematics

Modulation or Amplitude Equations are a universal tool to approximate solutions of complicated systems like partial or stochastic partial differential equations SPDEs near a change of stability when there is no center manifold theory available One can rely on the natural separation of time scales at the bifurcation to show that the solution of the original equation is well described by the bifurcating pattern with an amplitude that is slowly modulated in time and also in space if the underlying domain is sufficiently large This amplitude satisfies an equation on the slow time and space scale which is called Amplitude or Modulation Equation This is useful to explain qualitatively noise induced pattern formation below the change of stability and stabilization i e destruction of pattern due to degenerate additive noise The approach is on a formal level well known in the physics literature and for partial differential equations on unbounded domains rigorously studied in the last two decades Although the results for stochastic equations are far more general for simplicity of presentation we focus mostly on the less technical stochastic Swift Hohenberg equation and as an example the convective instability in Rayleigh Benard convection News Computer klüger als der Mensch

Original URL path: http://horst.qfl-berlin.de/stochastic-dynamics-near-change-stability-amplitude-and-modulation-equations (2016-04-24)

Open archived version from archive