Related papers: Dual representations for systemic risk measures ba…
In our previous paper, "A Unified Approach to Systemic Risk Measures via Acceptance Set" (\textit{Mathematical Finance, 2018}), we have introduced a general class of systemic risk measures that allow for random allocations to individual…
The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of…
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for…
In this paper, we deal with risk evaluation and risk-averse optimization of complex distributed systems with general risk functionals. We postulate a novel set of axioms for the functionals evaluating the total risk of the system. We derive…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
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 analyze in greater detail Conditional Shortfall…
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first…
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 study properties of certain risk measures associated with acceptance sets. These sets describe regulatory preconditions that have to be fulfilled by financial institutions to pass a given acceptance test. If the financial…
The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of…
We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…
Systemic risk measures play a crucial role in analyzing individual losses conditional on extreme system-wide disasters. In this paper, we provide a unified asymptotic treatment for systemic risk measures. First, we classify them into two…
We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have…
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…
We present simple general conditions on the acceptance sets under which their induced monetary risk and deviation measures are comonotonic additive. We show that acceptance sets induce comonotonic additive risk measures if and only if the…
The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and…