Stochastic Analysis and Stochastic Finance Seminar

Probabilistic Representation for Viscosity Solution of Fully nonlinear Stochastic PDEs

Speaker(s): 
Anis Matoussi (Universite du Maine, Le Mans)
Date: 
Thursday, May 12, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator, and we investigate the links between the 2BDSDEs and a class of parabolic fully nonlinear Stochastic PDEs. Precisely, we show that the Markovian solution of 2BDSDEs provide a probabilistic interpretation of the classical and stochastic viscosity solution of fully nonlinear SPDEs. This presentation includes some applications in pathwise stochastic control problems.

Asymptotic Lower Bounds for Optimal Tracking a Linear Programming Approach

Speaker(s): 
Mathieu Rosenbaum (Université Pierre et Marie Curie, Paris 6)
Date: 
Thursday, April 28, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We consider the problem of tracking a target whose dynamics is modeled by a continuous Ito semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control problem of Brownian motion, which is characterized as a deterministic linear programming. A comprehensive list of examples with explicit expressions for the lower bounds is also provided. This is joint work with Jiatu Cai and Peter Tankov.

Multivariate shortfall risk allocation and systemic risk

Speaker(s): 
Antonis Papapantoleon (TU Berlin)
Date: 
Thursday, February 11, 2016 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the computation of an overall reserve level and its allocation to the different components according to their systemic relevance.

Model Uncertainty, Fréchet Bounds and Applications in Option Pricing

Speaker(s): 
Thibaut Lux (TU Berlin)
Date: 
Thursday, February 11, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We consider the problem of finding arbitrage bounds for option prices of multi-asset options (i.e. options on multiple underlyings) in the case when partial information of the assets' probability distribution is available. We focus on the case in which the one-dimensional marginal distribution of each individual asset is known while also partial information on the dependence structure between the assets is available. This is in the literature often referred to as dependence uncertainty.

Robust super-hedging of options on VIX and martingale optimal transport

Speaker(s): 
Stefano De Marco (CMAP, Ecolé Polytechnique)
Date: 
Thursday, January 28, 2016 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

VIX options traded on the CBOE have become popular volatility derivatives. In this work, we bound VIX options from S\&P500 vanilla options and VIX futures. This leads us to introduce a new martingale optimal transport problem with additional constraints (that can eventually be solve numerically). Analytical lower and upper bounds are also provided, which highlight some (potential) arbitrage opportunities.

Deloitte & Touche GmbH Wirtschaftsprüfungsgesellschaft

Speaker(s): 
Dr. Jörg Kienitz, Director (Deloitte Düsseldorf)
Dr. Karl F. Bannör, Manager (Deloitte Berlin)
Date: 
Thursday, January 14, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Bewertung von exotischen Derivaten, Modellierung von Finanzkennzahlen, Quantifizierung von Markt- und Kreditrisiken, Erfüllen von regulatorischen Anforderungen, Entwicklung von quantitativen Tools – die Liste an Tätigkeiten im Quantitative-Finance-Bereich liest sich lang und abwechslungsreich. Wir laden Sie zu einem Workshop ein, bei dem sie erste Praxisluft aus dem Beratungsalltag schnuppern können.

Nash equilibria of threshold type for two-player nonzero-sum games of stopping

Speaker(s): 
Giorgio Ferrari (Universität Bielefeld)
Date: 
Thursday, December 17, 2015 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

In this talk I consider two-player nonzero-sum games of optimal stopping on a class of regular diffusions with singular boundary behaviour (in the sense of Itô and McKean, p. 108). I show that Nash equilibria are realised by stopping the diffusion at the first exit time from suitable intervals whose boundaries solve a system of algebraic equations. Under mild additional assumptions we also prove uniqueness of the equilibrium.

Volatility estimation under one-sided errors with applications to limit order books

Speaker(s): 
Markus Bibinger (Universität Mannheim)
Date: 
Thursday, December 17, 2015 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We consider a semi-martingale which forms a stochastic boundary, where we have discrete observations with one-sided errors. A rate-optimal estimator of the quadratic variation is constructed. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive n 1=3 as optimal (minimax) convergence rate in a high-frequency framework with n observations (in mean).

Backward Stochastic Partial Differential Equations in Hölder Spaces

Speaker(s): 
Wenning Wei (Fudan University)
Date: 
Thursday, December 3, 2015 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

My talk is concerned with solution in Hölder spaces for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown functional variables are viewed as deterministic time-space functionals, but take values in Banach spaces of random (vector) variables or processes. We define suitable functional Hölder spaces for them and give some inequalities among these Hölder norms. The existence, uniqueness as well as the regularity of solutions are proved for BSPDEs, which contain new assertions even on deterministic PDEs.

Generalized Dynkin games and game options in an imperfect market with default

Speaker(s): 
Roxana Dumitrescu (HU Berlin)
Date: 
Thursday, December 3, 2015 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

In the first part of the talk, we introduce a generalized Dynkin game problem with non linear conditional expectation induced by a Backward Stochastic Differential Equation (BSDE) with jumps. Under Mokobodski's condition, we establish the existence of a value function for this game. This value can be characterized via a doubly reflected BSDE. Using this characterization, we provide some new results on these equations, such as comparison theorems and a priori estimates. When the obstacles are left upper semicontinuous along stopping times, we prove the existence of a saddle point.

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