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arXiv · 2207.03710

Non-linear Affine Processes with Jumps

Francesca Biagini·Georg Bollweg·Katharina Oberpriller
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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.

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Francesca Biagini, Georg Bollweg, Katharina Oberpriller. 2022-07-08. Non-linear Affine Processes with Jumps. https://arxiv.org/abs/2207.03710

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