Related papers: Set-valued risk measures for conical market models
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…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent…
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…
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…
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…
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…
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…
Since the quasiconvex risk measures is a bigger class than the well known convex risk measures, the study of quasiconvex risk measures makes sense especially in the financial markets with volatility. In this paper, we will study the…
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…
New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any…
A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ assets with transaction costs or illiquidity and possible trading constraints are considered on a…
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.…
The relationship between set-valued risk measures for processes and vectors on the optional filtration is investigated. The equivalence of risk measures for processes and vectors and the equivalence of their penalty function formulations…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
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…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures.…
In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of…
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…