Affine processes beyond stochastic continuity

TL;DR

This paper extends the theory of affine processes to include cases with jumps that are either predictable or inaccessible, providing a comprehensive framework for such time-inhomogeneous affine semimartingales.

Contribution

It develops a general theory for finite-dimensional affine semimartingales with weak assumptions, including cases with non-stochastic continuity, and provides existence results and applications.

Findings

Affine semimartingale characteristics have affine form.

Conditional characteristic functions solve Riccati-type measure differential equations.

Existence of affine Markov processes and semimartingales under mild conditions.

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.