Building upon the dynamic programming principle for set valued functions arising from many
applications, in this paper we propose a new notion of set valued PDEs. The key component …

In this paper we study the path-regularity and martingale properties of the set-valued
stochastic integrals defined in our previous work Ararat et al.(2023). Such integrals have …

▶ A motivating example: An investor in an int'l economy faces two goods (domestic (A) and
foreign (B)). Rules of comparison:(A, B) is preferred over another pair only if A-amount has …

The integral representation theorem for martingales has been widely used in probability
theory. In this work, we propose and prove a general representation theorem for a class of …

In this study, we consider set-valued Lévy-driven Volterra-type stochastic integrals, defined
as the closed decomposable hull of convoluted integral functionals. In addition to the well …

In this paper, we discuss a general multidimensional linear convex stochastic control
problem with nondifferentiable objective function, control constraints, and random …

Building upon the dynamic programming principle for set valued functions arising from many
applications, in this paper we propose a new notion of set valued PDEs. The key component …

The overarching goal of this paper is to establish a set-valued It\^{o}'s formula. As an
application, we obtain the existence and uniqueness of solutions for the general set-valued …

In this paper, we prove necessary and sufficient conditions for the viability for an impulsive
stochastic functional differential inclusion driven by a fractional Brownian motion. The viable …