Related papers: Quasiconvex risk measures with markets volatility
Precise asymptotics for moderate deviation probabilities are established for open convex sets in both the finite- and infinite-dimensional settings. Our results are based on the existence of dominating points for these sets, a related…
Market liquidity plays a vital role in the field of market micro-structure, because it is the vigor of the financial market. This paper uses a variable called convexity to measure the potential liquidity provided by order-book. Based on the…
We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive 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…
We show that some specific market risk measures implied by current international capital regulation (the Basel Accords and the Capital Adequacy Directive of the European Union) violate the obvious requirement of convexity in some regions in…
Risk measure is a fundamental concept in finance and in the insurance industry, it is used to adjust life insurance rates. In this current paper, we will study dynamic risk measures by means of backward stochastic Volterra integral…
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 characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is…
In real-world decision-making problems, for instance in the fields of finance, robotics or autonomous driving, keeping uncertainty under control is as important as maximizing expected returns. Risk aversion has been addressed in the…
Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to…
Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems to be the correct language to describe…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility…
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…
This paper proposes RiskRank as a joint measure of cyclical and cross-sectional systemic risk. RiskRank is a general-purpose aggregation operator that concurrently accounts for risk levels for individual entities and their…
This paper relates the lower semi-continuity of an integral functional in the compensated compactness setting of vector fields satisfying a constant-rank first-order differential constraint, to closed $\mathcal{A}$-$p$ quasiconvexity of the…
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…
In this work we study the Lebesgue property for convex risk measures on the space of bounded c\`adl\`ag random processes ($\mathcal{R}^\infty$). Lebesgue property has been defined for one period convex risk measures in \cite{Jo} and earlier…
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…
Motivated by the results of static monetary or star-shaped risk measures, the paper investigates the representation theorems in the dynamic framework. We show that dynamic monetary risk measures can be represented as the lower envelope of a…