Related papers: Strongly Consistent Multivariate Conditional Risk …
This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our…
This paper develops a unified framework for the robustification of risk measures beyond the classical convex and cash-additive setting. We consider general risk measures on Lp spaces and construct their robust counterparts through families…
We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is…
Our purpose is to obtain a very effective and general method to prove that certain $C_0$-semigroups admit invariant strongly mixing measures. More precisely, we show that the Frequent Hypercyclicity Criterion for $C_0$-semigroups ensures…
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences…
We present a framework for constructing multivariate risk measures that is inspired from univariate Optimized Certainty Equivalent (OCE) risk measures. We show that this new class of risk measures verifies the desirable properties such as…
We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…
We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p<\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical…
The main goal of this paper is to investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo \cite{detlef-scandolo} and inspired by their result, we give a…
We provide a dual characterisation of the weak$^*$-closure of a finite sum of cones in $L^\infty$ adapted to a discrete time filtration $\mathcal{F}_t$: the $t^{th}$ cone in the sum contains bounded random variables that are…
In this paper we introduce and study the class of multivariate strong and strongly subexponential distributions. Some first properties are verified, as for example a type of multivariate analogue of Kesten's inequality, the closure property…
In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…
We prove a strong law of large numbers for a class of strongly mixing processes. Our result rests on recent advances in understanding of concentration of measure. It is simple to apply and gives finite-sample (as opposed to asymptotic)…
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…
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…
We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…
The familiar cascade measures are sequences of random positive measures obtained on $[0,1]$ via $b$-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values.…
In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property, which was introduced in [17], seems to be most suitable to ensure nice dual representations of risk…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
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…