Asset Partitioning and Financial Innovation

Review of the article by Ofer Eldar and Andrew Verstein titled “The Enduring Distinction between Business Entities and Security Interests”, 92 Southern California Law Review, no. 2 (2019)

Surveillance system and method having parameter estimation and operating mode partitioning

A system and method for monitoring an apparatus or process asset including partitioning an unpartitioned training data set into a plurality of training data subsets each having an operating mode associated thereto; creating a process model comprised of a plurality of process submodels each trained as a function of at least one of the training data subsets; acquiring a current set of observed signal data values from the asset; determining an operating mode of the asset for the current set of observed signal data values; selecting a process submodel from the process model as a function of the determined operating mode of the asset; calculating a current set of estimated signal data values from the selected process submodel for the determined operating mode; and outputting the calculated current set of estimated signal data values for providing asset surveillance and/or control

The New Business Entities in Evolutionary Perspective

The many legal forms for business organizations that first appeared in the U.S. during the last thirty years - the Limited Liability Company (LLC), the Limited Liability Partnership (LLP), the Limited Liability Limited Partnership (LLLP), and the statutory Business Trust - all combine the pattern of creditors' rights, or asset partitioning, that is traditional to the business corporation with the freedom of contract among investors and managers that is traditional to the partnership. To view these new entities as partnership-like is to treat the degree of freedom of contract as the essential difference between the traditional corporation and partnership forms; to view them as corporation-like is to treat the pattern of creditors' rights as the essential difference. While recent scholarship often takes the former view, the latter seems more accurate. History shows that much of the contractual inflexibility in the traditional corporation served merely to buttress its pattern of creditors' rights, and that this inflexibility fell away upon the development of substitute sources of investor protection. The new forms are thus better understood as part of a continuing development of the corporate form rather than as entities more akin to the traditional partnership, which has in fact been evolving in a different direction. The essay first develops this argument in terms of the tradeoff between contractual freedom and the form of asset partitioning that to date has received the most scholarly attention - that is, limited liability. It then explores the evolution of the new forms from a less familiar perspective, focusing on the entity shielding component of asset partitioning

Partitioning Procedure for Polynomial Optimization: Application to Portfolio Decisions with Higher Order Moments

We consider the problem of finding the minimum of a real-valued multivariate polynomial function constrained in a compact set defined by polynomial inequalities and equalities. This problem, called polynomial optimization problem (POP), is generally nonconvex and has been of growing interest to many researchers in recent years. Our goal is to tackle POPs using decomposition. Towards this goal we introduce a partitioning procedure. The problem manipulations are in line with the pattern used in the Benders decomposition [1], namely relaxation preceded by projection. Stengle’s and Putinar’s Positivstellensatz are employed to derive the so-called feasibility and optimality constraints, respectively. We test the performance of the proposed method on a collection of benchmark problems and we present the numerical results. As an application, we consider the problem of selecting an investment portfolio optimizing the mean, variance, skewness and kurtosis of the portfolio.Polynomial optimization, Semidefinite relaxations, Positivstellensatz, Sum of squares, Benders decomposition, Portfolio optimization