Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Für den Bereich Statistik

P. BANK, D. BECHERER, P.K. FRIZ, H. FöLLMER, U. HORST, P. IMKELLER, M. KELLER-RESSEL, U. KüCHLER, M. KUPPER, A. PAPAPANTOLEON

Ort

HU Berlin, Institut für Mathematik, Johann von Neumann - Haus, Rudower Chaussee 25, Hörsaal 1.115

Zeit

donnerstags, 16 Uhr / 17 c.t.

Interessenten sind herzlich eingeladen!

Programm

• 19. Oktober 2011 (Achtung: außerplanmäßiger Vortrag!)
  Frank Page (Indiana University, Bloomington)
  "Stationary Markov Equilibria in Discounted Stochastic Games"
  
  Abstract:
  While the existence of Nash equilibria in stationary Markov strategies for m-player, non-zero sum, discounted stochastic games with countable state spaces and compact metric action spaces has long been established (e.g., see Federgruen, 1978), the existence of such equilibria for the uncountable case has remained an open question since the problem was first analyzed by Himmelberg, Parthasarathy, Raghavan, and Van Vleck (1976). Beginning with Fudenberg and Levine (1983), Harris (1985), and Forges (1986), one of the striking insights to emerge from the literature on the existence of subgame perfect equilibria (SPE) in non-Markov (i.e., partly history-dependent) strategies in stage games with uncountable state spaces concerns the fundamental role played by public randomization devices in resolving existence problems in such games. The importance of public randomization devices for existence was then confirmed in an infinite horizon, stochastic game setting by Nowak and Raghavan (1992) and Duffie, Geanakoplos, Mas-Colell, and McLennan (1994) who showed that m-player, non-zero sum, uncountable-compact discounted stochastic games naturally possess stationary Markov correlated equilibria. Our main contribution is to establish the existence of stationary Markov equilibria (i.e., SPE in Markov stationary strategies) for this class of stochastic games, thus showing for the stationary Markov case that public randomization devices are not required for existence - and thus providing a positive resolution to a long-standing open question in stochastic games.
   
• 19. Oktober 2011 (Achtung: außerplanmäßiger Vortrag!)
  Sebastin Jaimungal (University of Toronto)
  "Self-Exciting Marked Point Processes for Algorithmic Trading"
  
  Abstract:
  In this I will present a class of self-effecting processes as a promising approach to modeling trading activity at high frequencies. Our model neatly accounts for the clustering of intensity of trades and the feedback effect which trading induces on both market orders as well as the shape of the limit order book (LOB). Further, it allows for efficient calibration to market data based on pseudo-likelihood methods. As well, various probabilistic quantities of interest such as the probability that the next market order is a buy or sell, the distribution of the time of arrival of a buy or sell order, and the probability that the mid-price moves a given amount before a market order arrives are also easily computable. Finally, we study an optimal control problem for a trader who places immediate-or-cancel limit buy-and-sell orders to take advantage of the bid-ask spread. Asymptotic expansions in the level of risk-aversion lead to closed form and intuitive results which are also adapted to the state of the market. Some numerical experiments will be used to demonstrate the utility of the model and optimal strategies. This is joint work with Alvaro Cartea, U. Carlos III de Madrid and Jason Ricci, U. Toronto
   
• 3. November 2011
  Igor Evstigneev (University of Manchester)
  "Von Neumann-Gale Dynamical Systems with Applications in Finance"
  
  Abstract:
  Von Neumann-Gale dynamical systems are defined in terms of multivalued operators possessing properties of convexity and homogeneity. These operators assign to each element of a given cone a convex subset of the cone describing possible one-step transitions from one state of the system to another. The classical, deterministic theory of such dynamics was originally aimed at the modelling of economic growth (von Neumann 1937 and Gale 1956). First attempts to build a stochastic generalization of this theory were undertaken in the 1970s by Dynkin, Radner and their research groups. However, the initial attack on the problem left many questions unanswered. Substantial progress was made only in the late 1990s, and final solutions to the main open problems were obtained only in the last four or five years. Recently it has been observed that stochastic analogues of von Neumann-Gale systems provide a natural and convenient framework for financial modelling (asset pricing and hedging under transaction costs). This observation gave a new momentum to studies in the field and posed new interesting questions. The talk will give an introduction into the theory, review recent progress and discuss applications.
   
• 3. November 2011
  N.N.
  tba
  
  
  Abstract:
  -
   
• 17. November 2011
  Georg Mainik (ETH Zürich)
  "Risk Diversification for Extremal Events: General Properties, Estimation, and Model Comparison"
  
  Abstract:
  The central topic of this talk is the diversification of catastrophic losses. Under the assumption of multivariate regular variation, the asymptotic portfolio loss distribution is characterized by a functional of the portfolio weights, the tail index, and the so-called spectral measure representing the dependence structure in the tail region. Further results encompass the general properties of the optimization problem, the estimation of the portfolio risk functional, and the ordering of models with respect to the asymptotic behaviour of portfolio losses. Particular interest is paid to the occurrence of negative diversification effects, compensation of gains and losses, uniform convergence of estimates, and the influence of dependence on model ordering.
   
• 17. November 2011
  Frank Lehrbass (RWE Supply and Trading GmbH)
  "Credit Risk at RWE Supply and Trading - An Overview"
  
  Abstract:
  The main concepts of credit risk are revisited from the perspective of a utility and a trading house. It will be made transparent how exposures to counterparties arise out of commodity business and what can be done to mitigate the credit risk. As concerns the remaining part of the credit risk it has to be priced. A discussion of the market for contingent Credit Default Swaps will be given. A glimpse at recent challenges of credit risk measurement and management will conclude.
   
• 1. Dezember 2011
  Eva Lütkebohmert (Universität Freiburg)
  tba
  
  
  Abstract:
  -
   
• 01. Dezember 2011
  Thorsten Schmidt (Technische Universität Chemnitz)
  tba
  
  
  Abstract:
  -
   
• 15. Dezember 2011
  Jan Werner (University of Minnesota)
  tba
  
  
  Abstract:
  -
   
• 15. Dezember 2011
  N.N.
  tba
  
  
  Abstract:
  -
   
• 12. Januar 2012
  Mathias Beiglböck (Universität München)
  tba
  
  
  Abstract:
  -
   
• 12. Januar 2012
  N.N.
  tba
  
  
  Abstract:
  -
   
• 26. Januar 2012
  Rüdiger Kiesel (Universität Duisburg-Essen)
  tba
  
  
  Abstract:
  -
   
• 09. Februar 2012
  Christoph Reisinger (University of Oxford)
  tba
  
  
  Abstract:
  -

Interessenten sind herzlich eingeladen.

Für Rückfragen wenden Sie sich bitte an:

Frau Sabine Bergmann

Mail: bergmann@mathematik.hu-berlin.de
Telefon: +49-30-2093-5811
Fax: +49-30-2093-5848
umboldt-Universität zu Berlin
Institut für Mathematik
Unter den Linden 6
10099 Berlin, Germany