## Invariance of closed convex cones for stochastic partial differential equations |

## Stefan Tappe, Freiburg |

## Thursday, 2018-01-25 17:00 |

The goal of this talk is to clarify when a closed convex cone is invariant for a stochastic partial differential equation (SPDE) driven by a Wiener process and a Poisson random measure, and to provide conditions on the parameters of the SPDE, which are necessary and sufficient. As a particular example, we will show how the Heath-Jarrow-Morton-Musiela (HJMM) equation from Financial Mathematics, which models the evolution of interest rate curves, fits into the present SPDE setting. Moreover, we will apply our result about the invariance of closed convex cones in order to investigate when the HJMM equation produces nonnegative interest rate curves. |