Humboldt Universität zu Berlin
Institut für Mathematik
Stochastik und Finanzmathematik

Stochastische Analysis und Stochastik der Finanzmärkte

Bereich für Stochastik

Ort: HU Berlin, Institut für Mathematik, Johann von Naumann - Haus, Rudower Chaussee 25, Hörsaal 1.115
Zeit: Donnerstag, 16 Uhr/17 c.t.
Interessenten sind herzlich eingeladen.

17. Oktober 2013 (16 Uhr c.t.)

17. Oktober 2013 (17 Uhr c.t.)
Michail Anthropelos (University of Piraeus)
An equilibrium model for commodity spot and forward prices
We consider a market model that consists of financial speculators and producers and consumers of a (consumption) commodity. Producers trade the forward contracts to hedge the commodity price uncertainty, while speculators invest in these contracts to diversify their portfolios. It is argued that the commodity equilibrium prices are the ones that clear out the market of spot and forward contracts. Assuming that producers and speculators are utility maximizers and that the consumers' demand and the exogenously priced financial market are driven by a Levy process, we provide expressions for the equilibrium prices and analyze their dependence on the model parameters.

31. Oktober 2013 (16 Uhr c.t.)
Christian Bayer (WIAS Berlin)
Simulation of conditional diffusions via forward--reverse stochastic representations
In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein et al. [Bernoulli 10(2):281-312, 2004] in the context of a forward-reverse transition density estimator. The corresponding Monte Carlo estimators have essentially root-N accuracy, hence they do not suffer from the curse of dimensionality. We provide a detailed convergence analysis and give a numerical example involving the realized variance in a stochastic volatility asset model conditioned on a fixed terminal value of the asset. (Joint work with John Schoenmakers.)

31. Oktober 2013 (17 Uhr c.t.)
Jinniao Qiu (HU Berlin)
Backward Stochastic Differential Evolutionary Systems with Singular Conditions and Optimal Portfolio Liquidation
In this talk, we shall first introduce a class of backward stochastic differential evolutionary systems (BSDES), which includes backward stochastic differential equations and backward stochastic partial differential equations with singular terminal conditions. By means of BSDESs with singular terminal conditions, we derive the optimal trading strategies for the optimal portfolio liquidation problems in which investors can simultaneously trade at a traditional exchange and in a dark market, under market impacts. When the liquidation problems are not Markovian, new stochastic dynamic models arise and some interesting properties will be presented. (Joint with Paulwin Graewe and Ulrich Horst)

14. November 2013 (16 Uhr c.t.)

14. November 2013 (17 Uhr c.t.)

28. November 2013 (16 Uhr c.t.)
Christoph Czichowski (London School of Economics and Political Science)
Strong Supermartingales and Portfolio Optimisation under Transaction Costs
In this talk, we develop a general duality theory for portfolio optimisation under proportional transaction costs with c\`adl\`ag price processes that are not necessarily semimartingales. In particular, we provide examples that illustrate the new effects arising from the combination of jumps of the price process and the transaction costs. The talk is based on joint work with Walter Schachermayer.

28. November 2013 (17 Uhr c.t.)
Shigeyoshi Ogawa (Ritsumeikan University)
On a stochastic Fourier transformation
For a certain class of random functions we introduce a stochastic Fourier transformation (SFT) via its stochastic Fourier coefficients (SFC). It was shown in very earlier articles of the author (eg. [1],[2]) that the SFT plays un essential role in the study of stochastic integral equations of Fredholm type. After 15 years the notion of SFC has reappeared implicitely in the study of volatility estimation due to P.Malliavin etal (eg. [3]). But many questions are left open conerning the SFC and SFT. Among them is the question of inversibility of the SFT. In this talk we discuss some basic properties of this stochastic transformation and show recent results (eg. [4],[5]) as well as its possible applications to mathematical sciences.
[1] Ogawa,S. : ''On the stochastic integral equation of Fredholm type'', in Pat- terns and Waves(monograph), Studies in Math and Its Appl.,(Kinokuniya), vol.18 (1986), pp.597606
[2] Ogawa,S. : ''On a stochastic integral equation for the random fields'', SĀ“eminaire de Proba., vol.25, Springer (1991), pp.324339
[3] Malliavin,P. and Thalmeyer,A. : ''Stochastic calculus of variations in mathematical finance'', Springer-Verlag (2006)
[4] Ogawa,S, ''On a stochastic Fourier transformation'', Stochastics Vol.85, 2013, 286 294
[5] Ogawa,S. and Uemura,H, ''On a stochastic Fourier coefficients'', J.Theo.Proba., (2013)

12. Dezember 2013 (16 Uhr c.t.)
Anis Matoussi (Universite du Maine)
Numerical scheme for quasilinear SPDE's via Backward doubly SDE's
We introduce forward-backward doubly SDEs and explain their connection to quasilinear stochastic partial differential equations (SPDEs in short). We then investigate a numerical probabilistic method for the solution of a class of quasilinear SPDEs. Our numerical scheme is based on discrete time approximation for solutions of systems of a decoupled forward-backward doubly stochastic differential equations. Under standard assumptions on the parameters, we prove the convergence and the rate of convergence of our numerical scheme.

12. Dezember 2013 (17 Uhr c.t.)
Claudio Fontana (INRIA Paris)
Insider trading, arbitrage profits and honest
In the context of a general continuous financial market model, we study whether the additional information associated with an honest time T gives rise to arbitrage profits. We show that an insider trader can typically realise arbitrage opportunities if the market does not close strictly before T, while arbitrages of the first kind can only be achieved by starting to trade as soon as T occurs. Finally, we discuss possible extensions of the theory to the case of general semimartingale models and arbitrary random times.

09. Januar 2014 (16 Uhr c.t.)
Stefan Ankirchner (Universität Bonn)
The Skorokhod embedding problem for homogeneous diffusions and applications to stopping contests
We consider the Skorokhod embedding problem (SEP) for a general time-homogeneous diffusion $X$: given a distribution $\rho$, is there a stopping time $\tau$ such that the stopped process $X$ has the distribution $\rho$? We present a solution method that makes use of martingale representations and draws on law uniqueness of weak solutions of SDEs. Then we ask if there exist solutions of the SEP which are respectively finite almost surely, integrable or bounded, and when does our proposed construc- tion have these properties. We provide conditions that guarantee existence of finite time solutions. Moreover, we fully characterize the distributions that can be embedded with integrable stopping times, and we derive necessary, respec- tively sufficient, conditions under which there exists a bounded embedding. Finally we apply the results to winner-take-all contests where agents aim at stopping a process at a highest possible value. The talk is based on joint work with David Hobson and Philipp Strack.

09. Januar 2014 (17 Uhr c.t.)
Ludowik Moreau (ETH Zürich)
Trading with Small Price Impact
An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. These results shed light on the general structure of the problem at hand, and also unveil close connections to optimal execution problems and to other market frictions such as proportional and fixed transaction costs.

23. Januar 2014 (16 Uhr c.t.)
Oleg Reichmann (ETH Zürich)

23. Januar 2014 (17 Uhr c.t.)
Alexander Giese (Unicredit Bank, München)

06. Februar 2014 (16 Uhr c.t.)

06. Februar 2014 (17 Uhr c.t.)

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