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Affine processes under parameter uncertainty

Fadina, Tolulope and Neufeld, Ariel and Schmidt, Thorsten (2019) 'Affine processes under parameter uncertainty.' Probability, Uncertainty and Quantitative Risk, 4 (1). ISSN 2367-0126

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Abstract

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.

Item Type: Article
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 12 Jan 2021 14:59
Last Modified: 12 Jan 2021 15:15
URI: http://repository.essex.ac.uk/id/eprint/28245

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