# American Institute of Mathematical Sciences

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Correction to: “Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting”
January  2019, 4: 5 doi: 10.1186/s41546-019-0039-1

## Affine processes under parameter uncertainty

 1. Department of Mathematical Stochastics, University of Freiburg, Ernst-Zermelo Str. 1, 79104 Freiburg, Germany; 2. Nanyang Technological University, Division of Mathematical Sciences, Singapore, Singapore; 3. Freiburg Institute of Advanced Studies(FRIAS), Freiburg im Breisgau, Germany; 4. University of Strasbourg Institute for Advanced Study(USIAS), Strasbourg, France

Received  June 20, 2018 Revised  April 23, 2019

We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call nonlinear affine processes. This is done as follows: given a set Θ of parameters for the process, we construct a corresponding nonlinear expectation on the path space of continuous processes. By a general dynamic programming principle, we link this nonlinear 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 Θ. This nonlinear affine process yields a tractable model for Knightian uncertainty, especially for modelling interest rates under ambiguity.
We then develop an appropriate Itô formula, the respective term-structure equations, and study the nonlinear versions of the Vasiček and the Cox-Ingersoll-Ross (CIR) model. Thereafter, we introduce the nonlinear Vasiček-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 this approach solves the modelling issue arising with negative interest rates.
Citation: Tolulope Fadina, Ariel Neufeld, Thorsten Schmidt. Affine processes under parameter uncertainty. Probability, Uncertainty and Quantitative Risk, 2019, 4 (0) : 5-. doi: 10.1186/s41546-019-0039-1