Stochastic Analysis and Stochastic Finance Seminar

Approximations of stochastic partial differential equations and applications in forward markets

Speaker(s): 
Andrea Barth (IANS Stuttgart)
Date: 
Thursday, December 4, 2014 - 4:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

In this talk I present a model for a yield curve in a forward market using 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 method to approximate the said weak error.

Martingale Optimal Transport

Speaker(s): 
H. Mete Soner (ETH Zürich)
Date: 
Thursday, November 20, 2014 - 5:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

In the original transport problem we are given two measures of equal mass and then look for an optimal map that takes one measure to the other one and also minimizes a given cost functional. Kantorovich relaxed this problem by considering a measure whose marginals agree with given two measures instead of a bijection. This generalization linearizes the problem. Hence, allows for an easy existence result and enables one to identify its convex dual. In robust hedging problems, we are also given two measures. Namely, the initial and the final distributions of a stock process.

Convex duality in continuous-time stochastic optimization

Speaker(s): 
Teemu Pennanen (King's College London)
Date: 
Thursday, November 20, 2014 - 4:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

We develop a duality framework for convex optimization problems over spaces of predictable stochastic processes. This is done by combining the conjugate duality theory of Rockafellar with some stochastic analysis. Various duality relations in stochastic control and mathematical finance are obtained as special cases. Besides classical models of financial markets, the general framework allows for e.g. illiquidity effects and portfolio constraints.

This is joint work with Ari-Pekka Perkkiö.

BSDEs of Counterparty Risk and Invariant Times

Speaker(s): 
Stéphane Crépey (Evry University)
Date: 
Thursday, November 6, 2014 - 4:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

This work is motivated by the need to generalize the classical credit risk reduced-form modeling approach for counterparty risk applications. We relax the basic immersion conditions of the classical approach by modeling the default time as an invariant time, such that local martingales with respect to a reduced filtration and a possibly changed probability measure, once stopped right before that time, stay local martingales with respect to the original model filtration and probability measure.

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?

Then consider working as a quant in the Quantitative Analytics Group at Barclays Investment Bank. Quants are responsible for developing and implementing core analytics used within the Investment Bank as well as helping the desk to manage the risk.

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.

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