A time inhomogeneous Cox-Ingersoll-Ross diffusion with jumps

TL;DR

This paper studies a complex financial model combining time-varying interest rate dynamics with jumps, providing mathematical solutions and probabilistic interpretations for its behavior.

Contribution

It introduces a novel time inhomogeneous Cox-Ingersoll-Ross model with jumps and proves the existence of a unique strong solution under specific conditions.

Findings

Laplace transforms for transition probabilities derived

Interpretation of results as limits of Gamma law mixtures

Existence of a unique strong solution established

Abstract

We consider a time inhomogeneous Cox-Ingersoll-Ross diffusion with positive jumps. We exploit a branching property to prove existence of a unique strong solution under a restrictive condition on the jump measure. We give Laplace transforms for the transition probabilities, with an interpretation in terms of limits of mixtures over Gamma laws.