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Keywords:

  • multivariate elliptic processes;
  • risk drivers;
  • sums-of-diffusions;
  • Lévy processes

We introduce and study multivariate elliptic processes, thus providing a dynamic counterpart to the (static) multivariate elliptic distributions. We pay special attention to the dynamics for Lévy processes and diffusions. We also discuss discrete versus continuous time modelling, jump processes versus diffusions, and semimartingales. Some data analysis illustrates the theory.