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Non-linear Affine Processes with Jumps

Author

Listed:
  • Francesca Biagini
  • Georg Bollweg
  • Katharina Oberpriller

Abstract

We present a probabilistic construction of $\mathbb{R}^d$-valued non-linear affine processes with jumps. Given a set $\Theta$ of affine parameters, we define a family of sublinear expectations on the Skorokhod space under which the canonical process $X$ is a (sublinear) Markov process with a non-linear generator. 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.

Suggested Citation

  • Francesca Biagini & Georg Bollweg & Katharina Oberpriller, 2022. "Non-linear Affine Processes with Jumps," Papers 2207.03710, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2207.03710
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    References listed on IDEAS

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    1. Tolulope Fadina & Ariel Neufeld & Thorsten Schmidt, 2018. "Affine processes under parameter uncertainty," Papers 1806.02912, arXiv.org, revised Mar 2019.
    2. Neufeld, Ariel & Nutz, Marcel, 2014. "Measurability of semimartingale characteristics with respect to the probability law," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3819-3845.
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