State Spaces of Multifactor Approximations of Nonnegative Volterra Processes

We show that the state spaces of multifactor Markovian processes, coming from approximations of nonnegative Volterra processes, are given by explicit linear transformations of the nonnegative orthant. We demonstrate the usefulness of this result for applications, including simulation schemes and partial differential equation methods for nonnegative Volterra processes. Funding: E. Abi Jaber gratefully acknowledges financial support from the Chaires Laboratoire de Finance des Marchés de l’Énergie-Finance et Développement Durable and Financial Risks at École Polytechnique. C. Bayer and S. Breneis gratefully acknowledge the support by the International Research Training Group 2544 “Stochastic Analysis in Interaction.” C. Bayer also acknowledges support from Deutsche Forschungsgemeinschaft Collaborative Research Center/Transregio 388 “Rough Analysis, Stochastic Dynamics and Related Fields” Project B02.