Affine processes under parameter uncertainty
A talk in the Bielefeld Stochastic Afternoon series by
Tolulope Fadina from University of Freiburg
| Abstract: | We develop a one-dimensional notion of affine processes under
parameter uncertainty, which we call non-linear affine
processes. This is done as follows: given a set $\Theta$ of
parameters for the process, we construct a corresponding non-linear
expectation on the path space of continuous processes. By a general
dynamic programming principle we link this non-linear expectation to a
variational form of the Kolmogorov equation, where the generator of a
single affine process is replaced by the supremum over all
corresponding generators of affine processes with parameters in
$\Theta$. This non-linear affine process yields a tractable model for
Knightian uncertainty, especially for modelling interest rates under
ambiguity.
We then develop an appropriate Ito-formula, the respective
term-structure equations and study the non-linear versions of the
Vasi\v cek and the Cox-Ingersoll-Ross (CIR) model. Thereafter we
introduce the non-linear Vasi\v cek-CIR model.
This model is particularly suitable for modelling interest rates when
one does not want to restrict the state space a priori and hence the
approach solves this modelling issue arising with negative interest
rates.
This is a joint work with Ariel Neufeld and Thorsten Schmidt. |