Principal Portfolios: Recasting the Efficient Frontier

A new method of analyzing the efficient portfolio problem under the assumption that short sales are allowed is presented. It is based on the remarkable finding that the original asset set can be reorganized as a set of uncorrelated portfolios, here named principal portfolios. The original problem of portfolio selection from the existing, correlated assets is thereby traded for the reduced problem of choosing from a set of uncorrelated portfolios. These portfolios constitute a new investment environment of uncorrelated assets, thereby providing significant conceptual and practical simplification in any portfolio optimization process such as the determination of the efficient frontier. The principal portfolio analysis of the efficient frontier reveals new features of the volatility structure of the optimal portfolios.

Hamilton-Jacobi Formulation of KS Entropy for Classical and Quantum Dynamics

A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action. This formulation is extended to the quantum domain using the Madelung-Bohm orbits associated with the Schroedinger equation. The resulting quantum KS invariant for a given orbit equals the mean decay rate of the probability density along the orbit, while its ensemble average measures the mean growth rate of configuration-space information for the quantum system.Comment: preprint, 8 pages (revtex

Reexamination of the A-J effect

We establish four necessary and sufficient conditions for the existence of the Averch-Johnson effect in a generalized version of their famous model of the rate-of-return regulated firm. The four necessary and sufficient conditions are then compared to the two stronger sufficient conditions for the Averch-Johnson effect found in the literature. Our analysis also permits us to put to rest a somewhat protracted debate about the very existence of the Averch-Johnson effect.

Correlative Capacity of Composite Quantum States

We characterize the optimal correlative capacity of entangled, separable, and classically correlated states. Introducing the notions of the infimum and supremum within majorization theory, we construct the least disordered separable state compatible with a set of marginals. The maximum separable correlation information supportable by the marginals of a multi-qubit pure state is shown to be an LOCC monotone. The least disordered composite of a pair of qubits is found for the above classes, with classically correlated states defined as diagonal in the product of marginal bases.Comment: 4 pages, 1 figur

Approximating Solutions for Ginzburg – Landau Equation by HPM and ADM

In this paper, an analytical approximation to the solution of Ginzburg-Landauis discussed. A Homotopy perturbation method introduced by He is employed to derive the analytic approximation solution and results compared with those of the Adomian decomposition method. Two examples are presented to show the capability of the methods. The results reveal that the methods are almost equally effective and promising