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December 2019 Affine processes beyond stochastic continuity
Martin Keller-Ressel, Thorsten Schmidt, Robert Wardenga
Ann. Appl. Probab. 29(6): 3387-3437 (December 2019). DOI: 10.1214/19-AAP1483

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.

Citation

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Martin Keller-Ressel. Thorsten Schmidt. Robert Wardenga. "Affine processes beyond stochastic continuity." Ann. Appl. Probab. 29 (6) 3387 - 3437, December 2019. https://doi.org/10.1214/19-AAP1483

Information

Received: 1 April 2018; Revised: 1 March 2019; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172338
MathSciNet: MR4047984
Digital Object Identifier: 10.1214/19-AAP1483

Subjects:
Primary: 60J25
Secondary: 91G99

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2019
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