This paper discusses and analyzes risk measure properties in order to understand how a risk measure has to be used to optimize the investor’s portfolio choices. In particular, we distinguish between two admissible classes of risk measures proposed in the portfolio literature: safety risk measures and dispersion measures. We study and describe how the risk could depend on other distributional pa...

Linear wave equations sourced by a Dirac delta distribution $\delta(x)$ and its derivative(s) can serve as model for many different phenomena. We describe discontinuous Galerkin (DG) method to numerically solve such with source terms proportional $\partial^n \delta /\partial x^n$. Despite the presence of singular terms, which imply or potentially solutions, our DG achieves global spectral accur...

we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

We consider a sequence of independent and identicaly distributed (iid) random variables with absolutely continuous distribution function F(x) and probability density function (pdf) f(x). Let Rnl be the largest observation after observing nth record and R(ns) be the smallest observation after observing the nth record. Then we say Wnr = Rnl− R(ns), n > 1, as the nth record range. We will c...

The capacity of distributional semantic models (DSMs) to discover similarities over large scale heterogeneous and poorly structured data brings them as a promising universal and low-effort framework to support semantic approximation and knowledge discovery. This position paper explores the role of distributional semantics in the Semantic Web vision, based on state-of-the-art distributional-rela...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Riemann, Lebesgue, Denjoy, Henstock–Kurzweil, McShane, Feynman, Bochner. There are well over 100 named integrals. Why so many? Some are of historical interest and have been superseded by better, newer ones. The Harnack integral is subsumed by the Denjoy. Some are equivalent, as are McShane and Lebesgue in Rn, and Denjoy, Perron, Henstock–Kurzweil in R. Some are designed to work in special space...

Benefit–cost analysis (BCA) evaluates governmental policies by summing individuals’ monetary equivalents, and is insensitive to distributional concerns. BCA does not take into account whether those made better off by a policy have higher or lower incomes, or higher or lower levels of nonincome welfare-relevant attributes (e.g., health), than those made worse off. Arguably, distributional consid...