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- Multi-dimensional quadratic BSDEs | Applied Financial Mathematics

to those BSDEs whose generators grow quadratically in the second unkown variable In this talk I will start with recalling J M Bismut s Ph D work on the linear quadratic optimal stochastic control problem and the introduction of backward stochastic Riccati equations which motivated the study of general quadratic BSDEs Then I review the theory of one dimensional quadratic BSDEs and show the difficulty in a general solution of multi dimensional quadratic BSDEs even when the terminal value is essentially bounded Finally I introduce our recent results jointed with Ying HU on adapted solution of a multi dimensional BSDE with a diagonall quadratic generator the quadratic part of whose i th component only depends on the i th row of the second unknown variable Local and global solutions are given which seem to be the first systematic positive results on the general solvability of multi dimensional quadratic BSDEs In our proofs it is crucial to apply both John Nirenberg and reverse Hölder inequalities for BMO martingales all details of which can be found in our online preprint arXiv 1408 4579 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/tba-14 (2016-04-24)

Open archived version from archive - Second order Pontriagin's principle for stochastic control problems / VORTRAG ENTFÄLLT ! | Applied Financial Mathematics

Bonnans INRIA Saclay Ecole Polytechnique We discuss stochastic optimal control problems whose volatility does not depend on the control and which have finitely many equality and inequality constraints on the expected value of function of the final state as well as control constraints The main result is a proof of necessity of some second order optimality conditions involving Pontryagin multipliers News Computer klüger als der Mensch Das vergessene Werkzeug der

Original URL path: http://horst.qfl-berlin.de/tba-20 (2016-04-24)

Open archived version from archive - Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty | Applied Financial Mathematics

Universität Bielefeld Under risk Arrow Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long lived securities We show that this result generically fails if there is Knightian uncertainty in the volatility Implementation is only possible if all discounted net trades of the equilibrium allocation are mean ambiguity free This is a joint work with Patrick Beissner News Computer klüger als der Mensch Das vergessene Werkzeug

Original URL path: http://horst.qfl-berlin.de/tba-21 (2016-04-24)

Open archived version from archive - The non-zero velocity regime of a random walk in random environment at low disorder | Applied Financial Mathematics

random walk in random environment at low disorder The non zero velocity regime of a random walk in random environment at low disorder 7 January 2015 Kategorie Research Seminars Rudower Chaussee 25 Room 1 115 6 p m Alejandro Ramirez Pontificia Universidad Católica de Chile We consider a random walk whose jump probabilities are i i d perturbations of those of the simple symmetric random walk This walk can exhibit a variety of behaviors ranging from recurrent to transient regimes with zero or non zero velocity Under the condition that the average jump after one step local drift is not too small it was proved by Sznitman that the random walk has a non zero velocity Using a renormalization approach we establish that under the same condition the velocity is asymptotically equal to the local drift as the strength of the perturbation vanishes This talk is based on a joint work with Clement Laurent and Christophe Sabot 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

Original URL path: http://horst.qfl-berlin.de/tba-15 (2016-04-24)

Open archived version from archive - Arbitrage-Free Pricing of XVA | Applied Financial Mathematics

Rudower Chaussee 25 Room 1 115 4 p m Agostino Capponi Columbia University New York We introduce a framework for computing the total valuation adjustment XVA of an European claim accounting for funding spreads counterparty risk and collateral mitigation We use no arbitrage arguments to derive the nonlinear backward stochastic differential equations BSDEs associated with the portfolios which replicate long and short positions in the claim This leads to defining buyer and sellers XVAs which in turn identify a no arbitrage band When borrowing and lending rates coincide our framework reduces to a generalized Piterbarg s model In this case we provide a fully explicit expression for the uniquely determined price of XVA When they differ we derive the semi linear partial differential equations PDEs associated with the non linear BSDEs We use them to conduct a numerical analysis showing high sensitivity of the no arbitrage band and replicating strategies to funding spreads and collateral levels This is joint work with Stephan Sturm and Maxim Bichuch 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/tba-18 (2016-04-24)

Open archived version from archive - Hawkes processes, microstructure and market impact | Applied Financial Mathematics

here Home Hawkes processes microstructure and market impact Hawkes processes microstructure and market impact 18 December 2014 Kategorie Research Seminars Rudower Chaussee 25 Room 1 115 5 p m Mark Hoffmann Université Paris Dauphine I will first shortly review the issue of obtaining simple lattice price models for assets observed at fine temporal scales that are 1 able to reproduce microstructure effects like variance noise or the Epps effect and 2 behave like continuous semimartingales compatible with the theory of arbitrage on large diffusive scales The use of mutually exciting point processes enable to track such microstruture effects across scales and I will present some recent and less recent models based on Hawkes processes In a second part I will show that beyond the attractivity of their analytical tractability Hawkes process enable to reproduce some market impact effects and exhibit simple links between market resilience and microstructure effects 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

Original URL path: http://horst.qfl-berlin.de/tba-19 (2016-04-24)

Open archived version from archive - Stable Processes: Absolute continuity and singularity under a purely discontinuous Girsanov transform | Applied Financial Mathematics

singularity of probability measures on the path space which are induced by an isotropic stable Lévy process and the purely discontinuous Girsanov transform of this process We also look at the problem of finiteness of the relative entropy of these measures An important tool is the question under which circumstances the a s finiteness of an additive functional at infinity implies the finiteness of its expectation Joint work with Zoran

Original URL path: http://horst.qfl-berlin.de/stable-processes-absolute-continuity-and-singularity-under-purely-discontinuous-girsanov-transform (2016-04-24)

Open archived version from archive - Approximations of stochastic partial differential equations and applications in forward markets | Applied Financial Mathematics

a stochastic partial differential equation driven by an infinite dimensional Lévy process This method is well known in interest rate theory To determine the price of an option one has to calculate the weak error of the solution to the stochastic partial differential equation The hyperbolic nature of this equation and the non continuous noise complicate the task of numerical approximation Furthermore I make use of a multilevel Monte Carlo

Original URL path: http://horst.qfl-berlin.de/approximations-stochastic-partial-differential-equations-and-applications-forward-markets (2016-04-24)

Open archived version from archive