Lévy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the Lévy driven Heath–Jarrow–Morton type term structure equation. This includes a full proof of existence and uniqueness in particular, which seems to have been lacking in the finance literature so far.

We study the existence of mild solutions for a class of impulsive fractional partial neutral stochastic integro-differential inclusions with statedependent delay. We assume that the undelayed part generates a solution operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for...

Abstract: This paper studies the existence of the mild solution for the neutral fractional integro-differential equation with nonlocal initial conditions in a Banach space. We obtain the sufficient condition for the existence results via fixed point theorem and approximate technique without assuming noncompactness or Lipschitz continuity of the nonlocal functions. We give an example for explain...

This paper is concerned with the existence of mild solution for impulsive stochastic differential equations with nonlocal conditions in PC -norm. Our approach is based on Krasnoselskii fixed point theorem. Mathematics subject classification (2010): 34K50, 60H15.

<p style='text-indent:20px;'>We discuss the existence and uniqueness of mild solutions for a class quasi-linear fractional integro-differential equations with impulsive conditions via Hausdorff measures noncompactness fixed point theory in Banach space. Mild solution controllability is discussed two particular cases.</p>