Related papers: A new view on risk measures associated with accept…
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable but also various economic scenarios. Motivated by this…
In this paper, we study general monetary risk measures (without any convexity or weak convexity). A monetary (respectively, positively homogeneous) risk measure can be characterized as the lower envelope of a family of convex (respectively,…
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic…
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional…
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which multiple risk-averse agents choose their decisions in such a way to minimize their individual accumulated…
The regulator is interested in proposing a capital adequacy test by specifying an acceptance set for firms' capital positions at the end of a given period. This set needs to be surplus-invariant, i.e., not to depend on the surplus of firms'…
A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub additive axiom to…
The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets…
We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both "first allocate, then aggregate" and "first aggregate, then allocate" type. In both…
We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…
We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We…
We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as…
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…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
We introduce the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk measure recovers, i.e., bounces back, when the risk-acceptance set is breached. We develop the corresponding…
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the…
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…