which allows for rich structural properties while retaining tractability due to the representation of the conditional characteristic function in terms of ordinary differential equations, the so called ’generalized Riccati equations’. In subsequent research further applications have been explored (e.g. [@KRPT2013; @Keller-Ressel2010; @Duffie05]) as well as extensions of the state space (e.g. [@CFMT2011; @CKMT2016]) and most notably an extension to time-inhomogeneous affine processes in [@Filipovic05].

In Remark 2.11 of [@Filipovic05] the author conjectures that his results can also be obtained on the level of semimartingales omitting the assumption of stochastic continuity. Here we confirm this conjecture by generalizing the result in [@Filipovic05] to affine semimartingales with singular continuous and discontinuous characteristics and only locally integrable parameters. This result is complemented by existence results for affine Markov processes and affine semimartingales under certain mild assumptions. Furthermore we provide a variety of examples and applications. In particular we propose an affine term-structure framework that allows for discontinuities at previously fixed time-points.

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The paper at hand is structured as follows. The next section revisits some facts about semimartingales before stating the definition of *affine semimartingales* and introducing certain technical assumption. After proving first results we define the concept of a *good parameter 