---
abstract: 'In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the corresponding semimartingale characteristics have affine form and that the conditional characteristic function can be represented with solutions to measure differential equations of Riccati type. We prove existence of affine Markov processes and affine semimartingales under mild conditions and elaborate on examples and applications including affine processes in discrete time.'
address:
- 'Albert-Ludwigs University of Freiburg, Ernst-Zermelo-Str. 1, 79104 Freiburg, Freiburg Research Institute of Advanced Studies (FRIAS), Germany, and University of Strasbourg Institute for Advanced Study (USIAS), France. '
- 'Dresden University of Technology, Zellescher Weg 12-14, 01069 Dresden, Germany.'
author:
- 'Martin Keller-Ressel'
- Thorsten Schmidt
- Robert Wardenga
date: 'December 21, 2018'
title: Affine processes beyond stochastic continuity
---

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Introduction
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The importance of jumps at predictable or predetermined times is widely acknowledged in the financial literature, see for example [@Merton1974; @GeskeJohnson84; @BelangerShreveWong2004; @Piazzesi2001; @Piazzesi2005; @KimWright; @DuffieLando2001; @Fama1970; @MillerRock1985]. This is due to the fact that a surprisingly 