Affine Volterra processes

Understand

We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients.

• Classical affine diffusions constitute a special case, but affine Volterra processes are neither semimartingales, nor Markov processes in general.
• We provide explicit exponential-affine representations of the Fourier-Laplace functional in terms of the solution of an associated system of deterministic integral equations of convolution type, extending well-known formulas for classical affine diffusions.
• For specific state spaces, we prove existence, uniqueness, and invariance properties of solutions of the corresponding stochastic convolution equations.