Limited liability and shares’ pricing: sufficient but not necessary

Limited liability has been seen as crucial for the development of capital markets. In this paper I use the CAPM to analyze how a company is priced differently under different liability regimes. I reach the conclusion that as far as the pricing and liquidity of shares is concerned, the positive features of a limited liability regime are common to “pro rata†unlimited liability. The prevalence of the unlimited liability regime over regimes of unlimited liability, prorata (or joint and several) should then be traced in other benefits that limiting liability may bring. Literature and history point to the relationship between bankruptcy procedures and liability regimes as the area where the limited liability regimes may be more cost effective and easier to implement.Corporation and Securities Law

The introduction of limited liability in nineteenth century England

In this paper I have analysed the development of company law from 1720 through to 1857. During this long period of time, company law assumed the characteristics it has now. At the starting point, company law stood with incorporation granted by the Crown or Parliament on one side and partnership regulated by common law on the other. The development of the modern corporation needed the definition of what were the problems connected to the fact that a firm is run in association and what is the legal framework that allows to solve efficiently with the lowest costs these problems. In this paper I show that the introduction of limited liability gets its meaning from the exact definition of many other aspects of company life, such as bankruptcy procedures, directors’ power and responsibility, shareholders rights, publicity regime for company acts. Accordingly it’s shown that the introduction of the limited liability regime can’t be studied in isolation and it was just the last step in a complex development process.Corporation and Securities Law

Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces.Comment: 86 pages, 15 figure

On the groundstate energy of tight knots

New results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are defined as tubular embeddings of the magnetic field in an ideal, perfectly conducting, incompressible fluid. An orthogonal, curvilinear coordinate system is introduced and the magnetic energy is determined by the poloidal and toroidal components of the magnetic field. Standard minimization of the magnetic energy is carried out under the usual assumptions of volume- and flux-preserving flow, with the additional constraints that the tube cross-section remains circular and that the knot length (ropelength) is independent from internal field twist (framing). Under these constraints the minimum energy is determined analytically by a new, exact expression, function of ropelength and framing. Groundstate energy levels of tight knots are determined from ropelength data obtained by the SONO tightening algorithm developed by Pieranski (Pieranski, 1998) and collaborators. Results for torus knots are compared with previous work done by Chui & Moffatt (1995), and the groundstate energy spectrum of the first prime knots (up to 10 crossings) is presented and analyzed in detail. These results demonstrate that ropelength and framing determine the spectrum of magnetic knots in tight configuration.Comment: 26 pages, 9 figure