Affine processes on positive semidefinite d×d matrices have jumps of finite variation in dimension d>1

The theory of affine processes on the space of positive semidefinite d×d matrices has been established in a joint work with Cuchiero et al. (2011) [4]. We confirm the conjecture stated therein that in dimension d>1 this process class does not exhibit jumps of infinite total variation. This constitutes a geometric phenomenon which is in contrast to the situation on the positive real line (Kawazu and Watanabe, 1971) [8]. As an application we prove that the exponentially affine property of the Laplace transform carries over to the Fourier–Laplace transform if the diffusion coefficient is zero or invertible.