Stochastic Analysis and Stochastic Finance Seminar

Duality for American options in non-dominated discrete-time models

Speaker(s): 
Xiaolu Tan (Université Paris Dauphine)
Date: 
Thursday, February 16, 2017 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

The classical pricing-hedging duality for American options with semi-static hedging does not hold in general in the simple formulation inherited from European option set-up. We propose two approaches to recover the duality result. The first approach consists in considering a bigger class of models and rendering an American option a European one. The second way is to relax the static trading and by allowing dynamic trading in the set of vanilla options.

A randomisation approach for the probabilistic representation and approximation of HJB equations

Speaker(s): 
Idris Kharroubi (CEREMADE - Universitè Paris)
Date: 
Thursday, February 2, 2017 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman-Kac representation by means of control randomization and backward stochastic differential equation with nonpositive jumps. We study a discrete time approximation for the minimal solution to this class of BSDE when the time step goes to zero, which provides both an approximation for the value function and for an optimal control in feedback form.

Stochastic invariance of closed sets with non-Lipschitz coefficients (and applications in finance)

Speaker(s): 
Bruno Bouchard (CEREMADE - Université Paris)
Date: 
Thursday, February 2, 2017 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

This talk provides a new characterization of the stochastic invariance of a closed subset with respect to a diffusion: we extend the well known inward pointing Stratonovich drift condition to the case where the diffusion matrix can fail to be differentiable (on the boundary). In particular, our result can be directly applied to construct affine diffusions and polynomial preserving diffusions on any arbitrary closed set.

Model-free Ito integration via pathwise super-hedging

Speaker(s): 
David Prömel (ETH Zürich)
Date: 
Thursday, January 12, 2017 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Using Vovk’s hedging based approach to mathematical finance, one can determine sample path properties of "typical price paths" belonging to the space of continuous functions or of non-negative càdlàg functions. Interestingly, all results for "typical price paths" hold quasi surely under all martingale measures. We prove that "typical price paths" possess quadratic variation and local limes. This allows us to develop model-free Itô integration as well as pathwise stochastic calculus for local times. This talk is based on joint works with R.M. Lochowski and N. Perkowski.

Risikocontrolling in der Versicherungswirtschaft - Die Solvency II Standardformel, Lineare Algebra und Diversifikation

Speaker(s): 
Joachim Paulusch (R+V Lebensversicherung AG, Risikocontrolling, Wiesbaden)
Date: 
Thursday, December 1, 2016 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Seit 01.01.2016 gilt das Aufsichtsregime Solvency II für alle Versicherungsunternehmen in Europa. Die Versicherungsunternehmen müssen eine sogenannte Solvenzkapitalanforderung berechnen und nachweisen, dass sie über Eigenmittel mindestens in Höhe der Solvenzkapitalanforderung verfügen. Dafür verwenden die meisten Versicherungsunternehmen die sogenannte Solvency II Standardformel. Wir untersuchen die Aggregation von Risiken in der Standardformel und beantworten die Fragen:

· Wie kann man Risikokapital in der Standardformel reallokieren, also fair auf Teilrisiken verteilen?

Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model

Speaker(s): 
Sergio Pulido (LaMME, ENSIIE, Université d'Evry Val d'Essonne)
Date: 
Thursday, December 1, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and derive their analyticexpansions for small risk aversion coefficients of the dealer. We briefly discuss related results that naturally arise when studying the replication and optimal investment problems under this model of price impact.

On portfolio optimization under small fixed transaction costs

Speaker(s): 
Jan Kallsen (Christian-Albrechts-Universität zu Kiel)
Date: 
Thursday, November 17, 2016 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

While optimal investment under proportional transaction costs is quite well understood by now, less has been done in the presence of fixed fees for any single transaction. In this talk we consider the asymptotics of the no-trade region for small fixed costs. More specifically, we sketch the rigorous verification for a general univariate Ito process market under exponential utility. (The talk is based on joint work with Mark Feodoria.)

Strong rate of convergence for the Euler-Maruyama approximation of SDES with irregular drift coefficient

Speaker(s): 
Olivier Pamen (University of Liverpool/AIMS Ghana)
Date: 
Thursday, November 17, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Model risk of contingent claims

Speaker(s): 
Natalie Packham (Hochschule für Wirtschaft und Recht Berlin)
Date: 
Thursday, October 20, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Paralleling regulatory developments, we devise value-at-risk and expected shortfall type risk measures for the potential losses arising from using misspecified models when pricing and hedging contingent claims. Essentially, P&L from model risk corresponds to P&L realized on a perfectly hedged position. Model uncertainty is expressed by a set of pricing models, each of which represents alternative asset price dynamics to the model used for pricing. P&L from model risk is determined relative to each of these models.

Additional information and pricing-hedging duality in robust framework

Speaker(s): 
Anna Aksamit (University of Oxford)
Date: 
Thursday, July 7, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

In robust approach, instead of choosing one model, one considers superhedging simultaneously under a family of models, or pathwise on the set of feasible trajectories. Usually in the literature the focus is on the natural filtration $\mathbb F$ of the price process. Here we extend that to a general filtration $\mathbb G$ including the natural filtration of the price process $\mathbb F\subset \mathbb G$. Two filtrations can model asymmetry of information on the market.

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