For a market with an atomless continuum of assets, we formulate the intuitive idea of a ‘‘well-diversified’’ portfolio, and present a notion of ‘‘exact arbitrage’’, strictly weaker than the more conventional notion of ‘‘asymptotic arbitrage’’, and necessary and sufficient for the validity of an APT pricing formula. Our formula involves ‘‘essential’’ risk, one based on a specific index portfolio...

Analytical gas-permeation models for predicting the separation process across  membranes (exit compositions and area requirement) constitutes an important and necessary step in understanding the overall performance of  membrane modules. But, the exact (numerical) solution methods suffer from the complexity of the solution. Therefore, solutions of nonlinear ordinary differential equations th...

the statistical analysis of spatial data is usually done under gaussian assumption for the underlying random field model. when this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. one of the crucial problems in this setting is specifying the block sizes. in this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the...

We show that the norm of the commutator defines “almost a metric” on the quotient space of commuting matrices, in the sense that it is a semi-metric satisfying the triangle inequality asymptotically for large matrices drawn from a “good” distribution. We provide theoretical analysis of this results for several distributions of matrices, and show numerical experiments confirming this observation.

The statistical analysis of spatial data is usually done under Gaussian assumption for the underlying random field model. When this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. One of the crucial problems in this setting is specifying the block sizes. In this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the...

We show that an asymptotic summation method, recently proposed by the authors, can be conveniently applied to slowly convergent power series whose coefficients are rational functions of the summation index. Several numerical examples are presented. 1. Asymptotic summation Consider a power series ∞ ∑

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.