Redaktion: K. Sigmund, G. Greschonig (Univ. Wien, Strudlhofgasse ...

Minisymposium Finanzmathematik
Affine Processes and their Applications in Finance
DAMIR FILIPOVIC
Dep. of Mathematics, ETH-Zürich
filipo@math.ethz.ch
http://www.math.ethz.ch/˜filipo
An affine process (AP) X is a Markov process with the property that, for every
t, the characteristic function of Xt is an exponential-affine function of the initial
state X0. 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.
On the problem of optimal investment with random
endowment in incomplete markets
DMITRY KRAMKOV
Carnegie Mellon University
Recently J. Cvitanic, W. Schachermayer and Wang H. studied the problem of optimal
investment with random endowment using a duality approach. In contrast
with the classical case (no endowment) the solution of the dual problem defined in
their paper exists provided its domain includes general linear functionals on L ∞ ,
i.e. finitely additive measures.
In this paper we formulate and study a new dual problem to the problem of optimal
investment with random endowment. This approach permits us to prove the
existence of the solution of the dual problem in L 1 , which is similar to the classical
case. Is is also useful for other applications in finance such as the utility based
pricing. The presentation is based on a joint project with Julian Hugonnier.
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