Infinite-dimensional Wishart processes
A talk in the SPDEs, optimal control and mean field games series by
Sonja Cox from Amsterdam
| Abstract: | A Wishart process is a time-homogeneous Markov process (Xt)t≥0 taking values in
the space of positive semi-definite matrices such that Xt has a (generalized)
Wishart distribution for every t ≥ 0. Wishart processes were introduced in
the '90s by Bru, in particular, it was shown that Wishart processes are affine
processes and solve certain SDEs. As such, Wishart processes have become a popular
choice for modelling stochastic covariance. For example, Wishart processes are
used in multi-dimensional Heston models to describe the instantaneous volatility
in a multi-dimensional stochastic differential equation. However, models for
energy and interest rate markets involve stochastic partial differential equations,
and thus call for infinite-dimensional covariance models. In our work, we introduce
and analyze infinite-dimensional Wishart processes, and discuss some of their
advantages and short-comings. |