Density and Occupation Bounds for Diffusions

17.06.2020 14:50 - 15:35

Paul Eisenberg (University of Liverpool)


Usually, uncertainty models assume that some coefficients are not or not precisely known but are inside a known set. A typical situation for the application of an uncertainty model in mathematical finance occurs when, for instance, the price flow of a risky asset is described via a diffusion but the drift and diffusion coefficients are not precisely known.
In this talk we consider a d-dimensional diffusion, i.e. a stochastic process of the form dX(t) = b(t) dt + a(t) dW(t)
where a,b are suitable stochastic integrands taking values in compact convex sets and W is a d-dimensional standard Brownian motion. We discuss bounds for the (Lebesgue-)density of X(t), if/when it exists, and for the expected occupation density of X(t).

Fakultät für Mathematik
Zoom Meeting