Related papers: Convex Risk Measures: Lebesgue Property on one Per…
We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient…
A radial probability measure is a probability measure with a density (with respect to the Lebesgue measure) which depends only on the distances to the origin. Consider the Euclidean space enhanced with a radial probability measure. A…
For a large class of symplectic integer matrices, the action on the torus extends to a symplectic $\mathbb{Z}^r$-action with $r\geq 2$. We apply this to the study of semiclassical measures for joint eigenfunctions of the quantization of the…
We consider the problem of finding Pareto-optimal allocations of risk among finitely many agents. The associated individual risk measures are law invariant, but with respect to agent-dependent and potentially heterogeneous reference…
This text grew out of notes I have used in teaching a one quarter course on integration at the advanced undergraduate level. My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to…
The metalog distributions represent a convenient way to approach many practical applications. Their distinctive feature is simple closed-form expressions for quantile functions. This paper contributes to further development of the metalog…
Let $S$ be a subset of $\mathbb{R}^d$ with finite positive Lebesgue measure. The Beer index of convexity $\operatorname{b}(S)$ of $S$ is the probability that two points of $S$ chosen uniformly independently at random see each other in $S$.…
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…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
In this paper, we study capital allocation for dynamic risk measures, with an axiomatic approach but also by exploiting the relation between risk measures and BSDEs. Although there is a wide literature on capital allocation rules in a…
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…
Multi-period measures of risk account for the path that the value of an investment portfolio takes. In the context of probabilistic risk measures, the focus has traditionally been on the magnitude of investment loss and not on the dimension…
We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good…
This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available…
The minimization of some multivariate risk indicators may be used as an allocation method, as proposed in C\'enac et al. [6]. The aim of capital allocation is to choose a point in a simplex, according to a given criterion. In a previous…
We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.
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…
The paper has 2 main goals: 1. We propose a variant of the CAPM based on coherent risk. 2. In addition to the real-world measure and the risk-neutral measure, we propose the third one: the extreme measure. The introduction of this measure…
We study submodularity for law-invariant functionals, with particular attention to convex risk measures. Expected losses are modular, and certainty equivalents are submodular exactly when the loss function is convex. Law-invariant coherent…