Related papers: Star-shaped Risk Measures
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear…
We present a general framework for measuring the liquidity risk. The theoretical framework defines a class of risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement…
Monitoring means to observe a system for any changes which may occur over time, using a monitor or measuring device of some sort. In this paper we formulate a problem of monitoring dates of maximal risk of a financial position. Thus, the…
We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis…
Geometrically convex functions constitute an interesting class of functions obtained by replacing the arithmetic mean with the geometric mean in the definition of convexity. As recently suggested, geometric convexity may be a sensible…
In the second part of our series we suggest new definitions of credit bond duration and convexity that remain consistent across all levels of credit quality including deeply distressed bonds and introduce additional risk measures that are…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
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…
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient…
Starting from the global financial crisis to the more recent disruptions brought about by geopolitical tensions and public health crises, the volatility of risk in financial markets has increased significantly. This underscores the…
We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of…
In this article we propose a generalization of the 2-dimensional notions of convexity resp. being star-shaped to symplectic vector spaces. We call such curves symplectically convex resp. symplectically star-shaped. After presenting some…
The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion…
It is known that each symmetric stable distribution in $R^d$ is related to a norm on $R^d$ that makes $R^d$ embeddable in $L_p([0,1])$. In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to…
We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk…
The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on $L^0$ is fixed to characterize the family of…
This paper derives -- considering a Gaussian setting -- closed form solutions of the statistics that Adrian and Brunnermeier and Acharya et al. have suggested as measures of systemic risk to be attached to individual banks. The statistics…
Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the…
We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…
This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of…