Universität zu Berlin
Stochastik und Finanzmathematik
Stochastische Analysis und Stochastik der Finanzmärkte
Bereich für Stochastik
P. BANK, D. BECHERER, P.K. FRIZ, H. FöLLMER, U. HORST, P. IMKELLER, M. KELLER-RESSEL, U. KüCHLER, A. PAPAPANTOLEON
Interessenten sind herzlich eingeladen.
- 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
- Simulation of conditional diffusions via forward--reverse
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
- 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
- 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. ,) 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. ). 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. ,) as well as its possible applications to mathematical
 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
 Ogawa,S. : ''On a stochastic integral equation for the random fields'', S´eminaire
de Proba., vol.25, Springer (1991), pp.324339
 Malliavin,P. and Thalmeyer,A. : ''Stochastic calculus of variations in mathematical
finance'', Springer-Verlag (2006)
 Ogawa,S, ''On a stochastic Fourier transformation'', Stochastics Vol.85, 2013, 286
 Ogawa,S. and Uemura,H, ''On a stochastic Fourier coefficients'', J.Theo.Proba.,
- 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
- 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
rise to arbitrage profits. We show that an insider trader can typically
arbitrage opportunities if the market does not close strictly before T,
arbitrages of the first kind can only be achieved by starting to trade as
as T occurs. Finally, we discuss possible extensions of the theory to the
of general semimartingale models and arbitrary random times.
- 09. Januar 2014 (16 Uhr c.t.)
- Stefan Ankirchner
- 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
- 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
- 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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