Stochastic Analysis and Stochastic Finance Seminar

Strong Supermartingales and Portfolio Optimisation under Transaction Costs

Speaker(s): 
Christoph Czichowski (London School of Economics and Political Science)
Date: 
Thursday, November 28, 2013 - 4:15pm
Location: 
Rudower Chaussee 25, Room 1.115

Simulation of conditional diffusions via forward--reverse stochastic representations

Speaker(s): 
Christian Bayer (WIAS Berlin)
Date: 
Thursday, October 31, 2013 - 4:15pm
Location: 
Rudower Chaussee 25, Room 1.115

An equilibrium model for commodity spot and forward prices

Speaker(s): 
Michail Anthropelos (University of Piraeus)
Date: 
Thursday, October 17, 2013 - 5:15pm
Location: 
Rudower Chaussee 25, Room 1.115

Decentralized Exchange

Speaker(s): 
Semyon Malamud (Ecole Polytechnique Fédérale de Lausanne)
Date: 
Thursday, July 4, 2013 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We develop an equilibrium model of decentralized trading that accommodates any coexisting exchanges including networks and more general, common market structures represented by hypergraphs. The model allows for any number of strategic traders and multiple divisible assets. We characterize equilibrium and welfare, and develop comparative statics with respect to preferences, assets, and market structures. Changes in market structure that increase price impact may increase total welfare.

Model-independent pricing and hedging in discrete time

Speaker(s): 
Beatrice Acciaio (London School of Economics)
Date: 
Thursday, July 4, 2013 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We study the problem of pricing and hedging path-dependent options in discrete time in a model-independent context. This means that no model is assumed for the underlying asset and no probabilistic structure is a priori given. The first issue to consider is the concept of arbitrage in such a framework. I will discuss the different notions of model-independent arbitrage so-far introduced in literature, and compare the results thereby obtained.

Risk measures for processes and BSDEs

Speaker(s): 
Irina Penner (HU Berlin)
Date: 
Thursday, June 20, 2013 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin

In the talk we analize risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for bounded cadlag processes, we show that this framework provides a systematic approach to the both issues of model ambiguity, and uncertainty about the time value of money. We also provide examples of such risk measures in terms of BSDEs, that depend on the whole path of a process.

Martingale Optimal Transport and Robust Hedging in Continuous Time

Speaker(s): 
Yan Dolinsky (Hebrew University of Jerusalem)
Date: 
Thursday, June 20, 2013 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity.

Asymptotic Independence of Three Statistics of the Maximal Increments of Random Walks and Lévy Processes

Speaker(s): 
Aleksandar Mijatovic (Imperial College London)
Date: 
Thursday, June 6, 2013 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

Let $H(x) = \inf\{n:\, \exists\, k x\}$ be the first epoch that an increment of the size larger than $x>0$ of a random walk $S$ occurs and consider the path functionals: $ R_n = \max_{m\in\{0, \ldots, n\}}\{S_{n} - S_m\}, R_n^* = \max_{m,k\in\{0, \ldots, n\}, m\leq k} \{S_{k}-S_m\}$ and $O_x=R_{H(x)}-x.$ The main result states that, under Cram\'{e}r's condition on the step-size distribution of $S$, the statistics $R_n$, $R_n^* -y$ and $O_{x+y}$ are asymptotically independent as $\min\{n,y,x\}\uparrow\infty$.

A Mathematical Treatment of Bank Monitoring Incentives

Speaker(s): 
Dylan Possamai (École Polytechnique in Paris)
Date: 
Thursday, June 6, 2013 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in by Pagès, with optimal contracting between competitive investors and an impatient bank monitoring a pool of long-term loans subject to Markovian contagion. We provide here a comprehensive mathematical formulation of the model and show using martingale arguments in the spirit of Sannikov, how the maximization problem with implicit constraints faced by investors can be reduced to a classic stochastic control problem.

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