  We consider affine Markov processes taking values in convex cones. In
particular, we characterize all affine processes taking values in an
irreducible symmetric cone in terms of certain L\'evy-Khintchine triplets. This
is the complete classification of affine processes on these conic state spaces,
thus extending the theory of Wishart processes on positive semidefinite
matrices, as put forward by Bru (1991).
