Related papers: Dual representations for systemic risk measures ba…

This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation.…

We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk…

We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that…

We study capacity accreditation of resource-colocated large loads, defined as large demands such as data center and manufacturing loads colocated with behind-the-meter generation and storage resources, synchronously connected to the bulk…

Decentralized trust management is used as a referral benchmark for assisting decision making by human or intelligence machines in open collaborative systems. During any given period of time, each participant may only interact with a few of…

Critical infrastructure systems must be both robust and resilient in order to ensure the functioning of society. To improve the performance of such systems, we often use risk and vulnerability analysis to find and address system weaknesses.…

Starting from an iterative and hence numerically easily implementable representation of the thin set of jumps of a c\`{a}dl\`{a}g adapted stochastic process $X$ (including a few applications to the integration with respect to the jump…

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main features are that they measure risk of processes that are functions of the history of a base…

Cooperative game theory studies how to allocate the joint value generated by a set of players. These games are typically analyzed using the characteristic function form with transferable utility, which represents the value attainable by…

We introduce a novel class of systemic risk measures, the Vulnerability Conditional risk measures, which try to capture the "tail risk" of a risky position in scenarios where one or more market participants is experiencing financial…

The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that…

We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…

Using elements from the theory of ergodic backward stochastic differential equations (BSDE), we study the behavior of forward entropic risk measures. We provide their general representation results (via both BSDE and convex duality) and…

It is often the case that risk assessment and prognostics are viewed as related but separate tasks. This chapter describes a risk-based approach to prognostics that seeks to provide a tighter coupling between risk assessment and fault…

This study introduces a new analytical framework for quantifying multivariate risk measures. Using the Wishart process, which is a stochastic process with values in the space of positive definite matrices, we derive several conditional tail…

Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a…

Risk management often plays an important role in decision making under uncertainty. In quantitative risk management, assessing and optimizing risk metrics requires efficient computing techniques and reliable theoretical guarantees. In this…

The multivariate conditional probability distribution models the effects of a set of variables onto the statistical properties of another set of variables. In the study of systemic risk in a financial system, the multivariate conditional…

We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…

This article considers the problem of risk-optimal allocation of security measures when the actuators of an uncertain control system are under attack. We consider an adversary injecting false data into the actuator channels. The attack…