Mathematical Finance Seminar
TU Berlin; MA042
Katharina Oberpriller (Ludwig-Maximilians-Universität München)

Reduced-form framework and affine processes with jumps under model uncertainty

We introduce a sublinear conditional operator with respect to a family of possibly non- dominated probability measures in presence of multiple ordered default times. In this way we generalize the results in [3] where a consistent reduced-form framework under model uncertainty for a single default is developed. Moreover, we present a probabilistic construction Rd-valued non-linear affine processes with jumps, which allows to model intensities in a reduced-form framework. This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation. This talk is based on [1] and [2].

[1] Francesca Biagini, Georg Bollweg, and Katharina Oberpriller. Non-linear affine processes with jumps. Probability, Uncertainty and Quantitative Risk, 8(3):235–266, 2023.
[2] Francesca Biagini, Andrea Mazzon, and Katharina Oberpriller. Reduced-form framework for multiple default times under model uncertainty. Stochastic Processes and Their Applications, 156:1–43, 2023.

[3] Francesca Biagini and Yinglin Zhang. Reduced-form framework under model uncertainty. The Annals of Applied Probability, 29(4):2481–2522, 2019