Related papers: Comonotonic measures of multivariate risks
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…
We propose a novel approach in the assessment of a random risk variable $X$ by introducing magnitude-propensity risk measures $(m_X,p_X)$. This bivariate measure intends to account for the dual aspect of risk, where the magnitudes $x$ of…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
Two new generalizations of the relation of comonotonicity of lattice-valued vectors are introduced and discussed. These new relations coincide on distributive lattices and they share several properties with the comonotonicity for the…
De Finetti's optimal reinsurance is a set of contracts, one for each risk in a portfolio, that caps the retained aggregate variance to a pre-specified level while minimizing total expected loss. The premiums are determined using the…
We deal with monotonic regression of multivariate functions $f: Q \to \mathbb{R}$ on a compact rectangular domain $Q$ in $\mathbb{R}^d$, where monotonicity is understood in a generalized sense: as isotonicity in some coordinate directions…
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…
The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are…
Acquisition of data is a difficult task in many applications of machine learning, and it is only natural that one hopes and expects the population risk to decrease (better performance) monotonically with increasing data points. It turns…
In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We…
We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev…
This paper addresses the importance of incorporating various risk measures in portfolio management and proposes a dynamic hybrid portfolio optimization model that combines the spectral risk measure and the Value-at-Risk in the mean-variance…
In this paper, we propose a novel association measure for longitudinal studies based on the traditional definition of relative risk. In a Markovian fashion, such a proposal takes into account the information content regarding the previous…
In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…
Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more…
We study a general contracting problem between the principal and a finite set of competitive agents, who perform equivalent changes of measure by controlling the drift of the output process and the compensator of its associated jump…
Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a…