## 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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