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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

FS Stochastische Analysis und Stochastik der Finanzmärkte

Bereich für Stochastik


P. BANK, D. BECHERER, P.K. FRIZ, H. FÖLLMER, U. HORST, P. IMKELLER, U. KÜCHLER, D. KREHER, N. PERKOWSKI


 
Ort: TU Berlin,
Institut für Mathematik,
Straße des 17. Juni 136, 10623 Berlin
Raum MA 313
 
Zeit: Donnerstag, 17 Uhr/18 Uhr c.t.
 

 

 

19.04.2018

(17 Uhr c.t.)

N.N.

 

19.04.2018

(18 Uhr c.t.)

N.N.

 

03.05.2018

 

Paris-Berlin Workshop

17.05.2018

(17 Uhr c.t.)

N.N.

 

17.05.2018

(18 Uhr c.t.)

N.N.

 

31.05.2018

(17 Uhr c.t.)

Jean-Pierre Fouque (University of California)

Optimal Portfolio under Fractional Stochastic Environment

 

Abstract: Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this talk, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index H 2 (0; 1)). We rigorously establish a first order approximation of the optimal value, when the return and volatility of the underlying asset are functions of a stationary slowly varying fractional Ornstein-Uhlenbeck process. We prove that this approximation can be also generated by the zeroth order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. Furthermore, we extend the discussion to general utility functions, and obtain the asymptotic optimality of this strategy in a speci c family of admissible strategies. If time permits, we will also discuss the problem under fast mean-reverting fractional stochastic environment.
Joint work with Ruimeng Hu (UCSB).

31.05.2018

(18 Uhr c.t.)

Thaleia Zariphopoulou (University of Texas at Austin)

Der Vortrag enfällt!

14.06.2018

(17 Uhr c.t.)

Sebastian Herrmann (University of Michigan)

Robust Pricing and Hedging around the Globe

 

Abstract: We study the martingale optimal transport duality for cadlag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of payo s that includes American, Asian, Bermudan, and  European options with intermediate maturity. We exhibit an optimal superhedging strategy for which the static part solves an auxiliary problem and the dynamic part is given explicitly in terms of the static part. In the case of nitely
supported marginal laws, solving for the static part reduces to a semi-in nite linear program.
This talk is based on joint work with Florian Stebegg (Columbia University).

14.06.2018

(18 Uhr c.t.)

Frédéric Abergel (Université de Paris Saclay)

Optimal order placement and limit order book modelling

 

Abstract: Optimal order placement is a key aspect of market making, and more generally, of liquidity
providing strategies in electronic markets. With this motivation in mind, we study the optimal placement
of limit orders from theoretical and numerical points of view, in the context of Markovian limit order book
models. The theoretically optimal strategies are then backtested using real data, providing results that
advocate for the design of better order book models. Some extensions are made, based either on Hawkes
processes, or on processes with nite memory (joint works with C. Hure, X. Lu, H. Pham).

28.06.2018

(17 Uhr c.t.)

Michael Kupper (Universität Konstanz)

Computation of optimal transport and related hedging problems via penalization and neural networks

Abstract: We present a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a nite dimensional one which corresponds to optimizing a neural
network with smooth objective function. We present  numerical examples from optimal transport, and bounds on the distribution of a sum of dependent random variables. As an application we focus on the problem of risk aggregation under model uncertainty. The talk is based on joint work with Stephan Eckstein and Mathias Pohl.

28.06.2018

(18 Uhr c.t.)

Wen Sun (University Pierre and Marie CURIE, Paris)

Large Urn Model with Local Mean-Field Interactions

Abstract: We study a large urn model connected by an underlying symmetrical graph. After some exponentially distributed amount of time all the balls of one of the urns are redistributed among the connected urns. The allocation of balls is done at random according to a set of weights which depend on the state of the system. The degree of the graph, which is the range of interaction, is assumed large, but is
not necessarily linear with respect to the number of urns. Moreover, the number of simultaneous jumps of the process is not bounded due to the redistribution of all balls of an urn at the same time. We describe the dynamic by using the local empirical distributions associated to the state of urns in the neighborhood of a given urn. Under some conditions, we are able to establish a mean- eld convergence result for this
measure-valued system. Convergence results of the  corresponding invariant distributions are obtained for
several classes of allocation policies. For the class of power of choices policies, we show that the invariant measure has an asymptotic nite support property when the average load per urn gets large. This result di ers somewhat from the classical double exponential decay property usually encountered in the literature for power of choices policies. This nite support property has interesting consequences in practice. (This is a joint work with Philippe Robert.)

12.07.2018

(17 Uhr c.t.)

Jinniao Qiu (University of Michigan)

Der Vortrag entfällt!

12.07.2018

(16 Uhr c.t.)

Eckhard Platen (University of Technology Sydney)

Dynamics of a Well-Diversified Equity Index and Martingale Inference

Abstract: The paper derives an endogenous model for the long-term dynamics of a well-diversi ed equity index with rough volatility, the S&P500. It assumes that the index is a proxy of the respective growth optimal portfolio, the variance of its increments evolves in some market time proportionally to the index value and the derivative of market time is a linear function of the squared derivative of a smoothed
proxy of the single driving Brownian motion. The resulting model is highly tractable, allows almost exact simulation and leads beyond classical nance theory. Its parameters are estimated via a novel martingale inference method, which employs higher-strong order, implicit approximations of the increments of the system of stochastic di erential equations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Interessenten sind herzlich eingeladen.

 

http://www.qfl-berlin.de/tags/stochastic-analysis-and-stochastic-finance-seminar

 


Für Rückfragen wenden Sie sich bitte an:

Frau Sabine Bergmann
bergmann@mathematik.hu-berlin.de
Telefon: 2093 5811
Telefax: 2093 5848

Verweise
Stochastik