15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung
16. bis 22. September 2001 in Wien
Minisymposium Finanzmathematik
Donnerstag, 20. September 2001, 16.10, Audimax der Universität Wien
Affine Processes and their Applications in Finance
Damir Filipovic, ETH Zürich
An affine process (AP) 
is a Markov process with the property that, for
every 
, the characteristic function of 
is an exponential-affine
function of the initial state 
. We discuss several consequences of this
definition. It can be shown that any AP is a Feller jump-diffusion process
with an affine generator. In the case where the state space D is the real
line, an AP is simply an Ornstein-Uhlenbeck type process. If D is the
positive half-line, an AP turns out to be a CBI (continuous state branching
with immigration)-process.
APs are widely used in financial applications, which is due to their
analytical tractability. We give a short overview of the classical papers in
the areas: term structure modelling, stochastic volatility option pricing
and intensity based modelling of default.
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