Research talks

• University of Angers, France, Conference Analyse Harmonique et Probabilities, September 2nd-7th, 2012
  
  "Advances in the Theory of Affine Processes".

Affine Processes are a special class of Markov processes in continuous time, which share a key feature: Their characteristic function is of exponentially affine form. This makes them analytically tractable and that's why they are much appreciated in e.g., financial modeling. There has recently been intense research on various existence, analytic and probabilistic issues of affine processes. In this talk I present some of the recent results from the theory of affine processes.


• University of Manchester, Business School, June 8 2012, 11:30
  
  "Affine Processes on Matrix State Spaces.

Affine processes on the cones of symmetric positive semidefinite d x d matrices have been characterized in joint work with Cuchiero, Filipovic and Teichmann (Annals of Applied Probabilitiy, 2011). In a recent work, I show that their jump behaviour is restricted to finite total variation, when d is greater than 1. This finding constitutes a multivariate pheonomenon as in one dimension it does not hold. This presentation should give a little insight into the affine model specification. It will not be too technical.


• University of Manchester, Business School, May 4th, 2012
  
  "Recursive Equations in Counterparty Credit Risk.
  On the foundations of Credit Value Adjustments, and their history
• University of Warwick, July 6th
  
  "Recursive Utility: Motivation, Basics and Approaches in Continuous Time."
  
  Invited by Paul Schneider.
  
  Introductory lecture at Warwick Business School's conference "Frontiers of Finance 2011".
• Dublin City University, June 27th
  
  "The rank condition for the family of Wishart distributions"
  
  Invited by Paolo Guasoni.
  
  "The probably most useful generalization of the gamma and chi-square distributions on the positive real line yields the class of non-central Wishart distributions on the cone of positive semi-definite matrices. I apply the recent theory of affine processes on positive semidefinite matrices [2] and derive nontrivial restrictions on shape and non-centrality parameter, incorporated in the so-called 'rank condition' [1]. This condition is a geometric one and it is empty in the one-dimensional case. Also, it is new, and it has never been conjectured in the literature. The research on affine processes has been (and still is) mainly motivated by financial applications (stochastic Co-volatility models, modeling of positive, stochastically correlated risk factors in credit risk...); this work shows that the involved mathematics can also prove useful for seemingly unrelated questions." Literature: [1] On the existence of non-central Wishart distributions, submitted (2011) [2] Affine processes on positive semidefinite matrices (with Christa Cuchiero, Damir Filipovic and Josef Teichmann), Annals of Applied Probability 2011, Vol. 21, No. 2, 397-463 2010.
• TU Berlin, June 23rd
  
  "On the validity of the affine transform formula in the presence of jumps"
  
  Invited by Martin Keller-Ressel and Michael Kupper (Humboldt University Berlin)
  
  In this talk I address the topic of Fourier pricing in the context of multivariate affine jump-diffusion processes. A series of connected joint works with Damir Filipovic, Martin Keller-Ressel and other colleagues have lead to a deep understanding of the affine property. They allow to use the extended affine transform formula when pricing contingent claims with Fourier-inversion as put forward by Carr and Madan in their 99' paper.
• Meeting on Self Similarity, Le-Touquet-Paris-Plage, June 6th
  
  " Wishart processes and Wishart distributions"
  
  Invited by Thomas Simon