We introduce a framework for quantifying propagation of uncertainty arising in a dynamic
setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete …

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 investigate possible approaches to study general time-inconsistent
optimization problems without assuming the existence of optimal strategy. This leads …

Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and
unlike the zero-sum case, they may have different values at different equilibriums. Instead of …

We investigate to which extent the relevant features of (static) Systemic Risk Measures can
be extended to a conditional setting. After providing a general dual representation result, we …

We study a dynamic stochastic control problem subject to Knightian uncertainty with multi-
objective (vector-valued) criteria. Assuming the preferences across expected multi-loss …

We introduce a new notion of conditional nonlinear expectation under probability distortion.
Such a distorted nonlinear expectation is not subadditive in general, so it is beyond the …

For time-inconsistent optimal control problems, a quite popular approach is the equilibrium
approach, taken by sophisticated agents. In this short note, we construct a deterministic …

Risk measures for random vectors have been considered in multiasset markets with
transaction costs and financial networks in the literature. While the theory of set-valued risk …

In this thesis we discuss possible approaches to study time-inconsistent optimization
problems without the presumption that the optimal strategy exists. This immediately leads to …