This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial applications are analyzed, such as extensions of the expected value premium principle when expected losses ar...

We present a novel method to compute expectation values in the Lieb-Liniger model both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that ru...

In this paper, we examine the problem of finding an optimal portfolio of securities by using the probability function of portfolio risk as a constraint. We obtain the value of the risk coefficient for which the problem of maximizing the expectation of the portfolio return with a probabilistic risk function constraint is equivalent to the maximizing the linear convolution of the criteria ”expect...

as the " W'-measure" of the holonomy determined by the oriented knot k . In this way every pair (G, W) defines a numerical invariant on knots by its expectation value (Xw{k)} in the k-G theory, and Witten argues that these expectation values are related to the values of the Jones and Alexander polynomials at various roots of unity. For instance, when G = SU'(2) and W is the representation of "l...

We show explicitly that the well-known Gouy phase shift of any focused beam originates from transverse spatial confinement, which, through the uncertainty principle, introduces a spread in the transverse momenta and hence a shift in the expectation value of the axial propagation constant. A general expression is given for the Gouy phase shift in terms of expectation values of the squares of the...

This paper introduces two constraints on the use of variables inside the expectation formula. The constraints are, roughly, (1) that the variable takes the same conditional expectation in each event in the partition and (2) that the total expected value be a linear function of the variable for each event in the partition. We argue that the reasoning in one version of the “two envelope paradox” ...

Let MaxCut(G) be the value of the maximum cut of a graph G. Let f(x, n) be the expectation of MaxCut(G)/xn for random graphs with n vertices and xn edges and let r(x, n) be the expectation of MaxCut(G)/xn for random 2x-regular graphs with n vertices. We prove, for sufficiently large x: 1. limn→∞ f(x, n) ≤ 12 + √ ln 2 2x , 2. limn→∞ r(x, n) ≤ 12 + 1 √ x + 1 2 ln x x .

Conformal field theory (CFT) is important in modern particle physics in various contexts. The most powerful tool in the 2-dimensional CFT is the operator product expansion (OPE). The OPE between the energy-momentum tensor and an operator extracts its conformal weight. We find it interesting to consider the similar issue with respect to the Wilson loop in a conformally invariant Yang-Mills theor...

The inference of entangled quantum states by recourse to the maximum entropy principle is considered in connection with the recently pointed out problem of fake inferred entanglement [R. Horodecki, et al., Phys. Rev. A 59 (1999) 1799]. We show that there are operators Â, both diagonal and non diagonal in the Bell basis, such that when the expectation value 〈Â〉 is taken as prior information the ...