Related papers: Set risk measures
In recent years, it has become apparent that an isolated microprudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost…
In this paper, we introduce a new class of set-valued risk measures, named set-valued star-shaped risk measures. Motivated by the results of scalar monetary and star-shaped risk measures, this paper investigates the representation theorems…
In order to evaluate the quality of the scientific research, we introduce a new family of scientific performance measures, called Scientific Research Measures (SRM). Our proposal originates from the more recent developments in the theory of…
We revisit the recently introduced concept of return risk measures (RRMs) and extend it by incorporating risk management via multiple so-called eligible assets. The resulting new class of risk measures, termed multi-asset return risk…
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…
Risk measures for random vectors have been considered in multi-asset markets with transaction costs and financial networks in the literature. While the theory of set-valued risk measures provide an axiomatic framework for assigning to a…
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 develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a…
Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach…
We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying…
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…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
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.…
In this paper, we consider a situation where a decision maker's (DM's) risk preference can be described by a spectral risk measure (SRM) but there is not a single SRM which can be used to represent the DM's preferences consistently.…
The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite…
In this note we consider a system of financial institutions and study systemic risk measures in the presence of a financial market and in a robust setting, namely, where no reference probability is assigned. We obtain a dual representation…