Stochastic Analysis and Stochastic Finance Seminar

Multilevel scheme for BSDEs

Speaker(s): 
Plamen Turkedjiev (CMAP, École Polytechnique Paris)
Date: 
Thursday, October 23, 2014 - 5:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

We develop a multilevel approach to compute approximate solutions to backward dierential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of rening time-grids to reduce statistical approximation errors in an adaptive and generic way. We provide an error analysis with explicit and non-asymptotic error estimates for the multilevel scheme under general conditions on the forward process and the BSDE data.

On the pathwise quadratic variation and local time

Speaker(s): 
Pietro Siorpeas (University of Vienna)
Date: 
Thursday, October 23, 2014 - 4:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

Föllmer has shown that one can obtain a pathwise Itô formula for paths which possess quadratic variation along a (fixed) sequence of partitions; this applies of course to a.e. path of any given semimartingale. Here we investigate the extent to which the quadratic variation can depend on the sequence of partitions. Then, we extend Wuermlis work and develop a pathwise Tanaka-Meyer formula for continuous paths which admit pathwise local time, which we prove to exist for a.e. path of a continuous semimartingale.

Affine processes from the perspective of path-space valued Levy processes

Speaker(s): 
Nicolleta Gabrielli (ETH Zurich)
Date: 
Thursday, July 17, 2014 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

Based on the theory of multivariate time change for Markov processes, we show how to identify affine processes as solutions of certain time change equations. More precisely, we are able to construct the paths of an affine process from the paths of a family of Levy processes properly time–changed. The approach relies on the construction of a universal transformation on the path-space transforming the laws of a family of Levy processes with no negative jumps to the law of an affine process.

Backward Stochastic Partial Differential Equations and their Application to Stochastic Black-Scholes Formula

Speaker(s): 
Qi Zhang (Fudan University)
Date: 
Thursday, July 17, 2014 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

The backward SPDEs, originated from the study of optimal control theory of SPDEs, can be applied to mathematical finance problems. We demonstrate their theoretical application to stochastic Black-Scholes formula, in a general setting to the parameters of the model. This application is based on our studies of the solvability to degenerate backward SPDEs without technical assumptions and their connection with forward-backward SDEs. The connection between backward SPDEs and forward-backward SDEs can also be regarded as an extension of Feynman-Kac formula to non-Markovian framework.

Barclays Company Presentation

Date: 
Thursday, July 3, 2014 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

Background in mathematics, physics or informatics? Are you interested in applying your analytical skills in a dynamic, fast paced environment with many development opportunities?

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Valuation in illiquid markets

Speaker(s): 
Ernst Eberlein (Albert-Ludwigs-Universität Freiburg)
Date: 
Thursday, June 19, 2014 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

After a long period with an abundance of liquidity in the markets, the 2007-2009 financial crisis illustrated in a dramatic way how fundamental liquidity risk is. In this situation many securities with an excellent rating could no longer be traded. What is the value of the instruments under these market conditions? The classical valuation theory which is based on the law of one price assumes implicitly that market participants can trade freely in both directions at the same price.

Fundamental theorem of asset pricing without reference measure

Speaker(s): 
Ludovic Tangpi (Universität Konstanz)
Date: 
Thursday, June 19, 2014 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

When a financial market is governed by a single probability measure, the absence of arbitrage opportunities is characterized by the existence of equivalent martingale or local martingale measures. In this talk, we focus on the fundamental theorem of asset pricing in the case where the market is governed by a non-dominated set of probability measures. We introduce the concept of free lunch with disappearing risk.

Efficient Laplace and Fourier inversions and Wiener-Hopf factorization in financial applications

Speaker(s): 
Sergei Levendorskii (University of Leicester)
Date: 
Thursday, June 5, 2014 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

Appropriate conformal deformations increase the speed and accuracy of calculation of fairly complicated oscillatory integrals in option pricing formulas in many cases when standard approaches are either too slow or

Estimate nothing

Speaker(s): 
Chris Rogers (University of Cambridge)
Date: 
Thursday, June 5, 2014 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Room MA041

In the econometrics of financial time series, it is customary to take some parametric model for the data, and then estimate the parameters from historical data. This approach suffers from several problems. Firstly, how is estimation error to be quantified, and then taken into account when making statements about the future behaviour of the observed time series?

Foundations of Risk Management and Consistency of Risk Measure Estimates

Speaker(s): 
Mark Davis (Imperial College London)
Date: 
Thursday, May 8, 2014 - 5:00pm
Location: 
TU Berlin, Raum MA 041, Straße des 17. Juni 136, 10623 Berlin

Recently there has been renewed debate about the relative merits of VaR and CVar as measures of financial risk, together with an increasing insistence that these issues cannot be meaningfully discussed without taking into account how the relevant values are to be computed. This prompts an enquiry into the basics of financial risk management, and it seems that key insights from other areas such as weather forecasting have been ignored by the financial community.

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