相关论文: On Jensen's inequality for generalized Choquet int…

Bi-capacities arise as a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours, encompassing models such…

With the help of Generalized Estimating Equations, we identify locally D-optimal crossover designs for generalized linear models. We adopt the variance of parameters of interest as the objective function, which is minimized using…

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…

Under expected utility the local index of absolute risk aversion has played a central role in many applications. Besides, its link with the "global" concepts of the risk and probability premia has reinforced its attractiveness. This paper…

We extend Dragomir's refinement of Jensen's inequality from the dicrete to the general case, identifying the equality conditions.

A sufficient condition for the convergence of a generalized formal power series solution to an algebraic $q$-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power…

We establish general "collapse to the mean" principles that provide conditions under which a law-invariant functional reduces to an expectation. In the convex setting, we retrieve and sharpen known results from the literature. However, our…

We derive computational formulas for the generalized Choquet integral based on the novel survival function introduced by M. Boczek et al. [1]. We demonstrate its usefulness on the Knapsack problem and the problem of accommodation options.…

Most people are risk-averse (risk-seeking) when they expect to gain (lose). Based on a generalization of ``expected utility theory'' which takes this into account, we introduce an automaton mimicking the dynamics of economic operations.…

We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Schroedinger-Robertson (SR) uncertainty…

Chen's iterated integrals may be generalized by interpolation of functions of the positive integer number of times which particular forms are iterated in integrals along specific paths, to certain complex values. These generalized iterated…

Groups of humans are often able to find ways to cooperate with one another in complex, temporally extended social dilemmas. Models based on behavioral economics are only able to explain this phenomenon for unrealistic stateless matrix…

Interchange theorems between minimization and integration are useful in optimization, especially in optimal control and in stochastic optimization. In this article, we establish a generalized minimization interchange theorem, where…

It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as…

The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of $[0,1]^n$. We take this basic fact as a starting point to define the Choquet integral in a very general way,…

We introduce a framework for systemic risk modeling in insurance portfolios using jointly exchangeable arrays, extending classical collective risk models to account for interactions. Joint exchangeability is a more general probabilistic…

In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their properties, a quantitative estimate for the nonlinear…

The paper that is commented by Touchette contains a computational study which opens the door to a desirable generalization of the standard large deviation theory (applicable to a set of $N$ nearly independent random variables) to systems…

The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Gr\"{u}ss Inequality. It has been reported in the literature that fragmentation (or…

The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen's $d$. A recently proposed generalized estimator allows conditioning on further independent variables…