Leptokurtic Portfolio Theory

The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurtic, because it minimises the effects from "fat tails" of returns. The leptokurtic portfolio theory provides an optimal portfolio for investors, who define their risk-aversion as unwillingness to experience sharp drawdowns in asset prices. Two types of risks in asset returns are defined: a fluctuation risk, that has Gaussian distribution, and a drawdown risk, that deals with distribution tails. These risks are quantitatively measured by defining the "noise kernel" -- an ellipsoidal cloud of points in the space of asset returns. The size of the ellipse is controlled with the threshold parameter: the larger the threshold parameter, the larger return are accepted for investors as normal fluctuations. The return vectors falling into the kernel are used for calculation of fluctuation risk. Analogously, the data points falling outside the kernel are used for the calculation of drawdown risks. As a result the portfolio optimisation problem becomes three-dimensional: in addition to the return, there are two types of risks involved. Optimal portfolio for drawdown-averse investors is the portfolio minimising variance outside the noise kernel. The theory has been tested with MSCI North America, Europe and Pacific total return stock indices.Comment: 10 pages, 2 figures, To be presented in NEXT-SigmaPh

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

Statistical Mechanics of maximal independent sets

The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and covering constraints. It is known that finding minimum and maximum-density maximal independent sets are hard optimization problems. In this paper, we use cavity method of statistical physics and Monte Carlo simulations to study the corresponding constraint satisfaction problem on random graphs. We obtain the entropy of maximal independent sets within the replica symmetric and one-step replica symmetry breaking frameworks, shedding light on the metric structure of the landscape of solutions and suggesting a class of possible algorithms. This is of particular relevance for the application to the study of strategic interactions in social and economic networks, where maximal independent sets correspond to pure Nash equilibria of a graphical game of public goods allocation

Statistical mechanics of complex economies

In the pursuit of ever increasing efficiency and growth, our economies have evolved to remarkable degrees of complexity, with nested production processes feeding each other in order to create products of greater sophistication from less sophisticated ones, down to raw materials. The engine of such an expansion have been competitive markets that, according to General Equilibrium Theory (GET), achieve efficient allocations under specific conditions. We study large random economies within the GET framework, as templates of complex economies, and we find that a non-trivial phase transition occurs: the economy freezes in a state where all production processes collapse when either the number of primary goods or the number of available technologies fall below a critical threshold. As in other examples of phase transitions in large random systems, this is an unintended consequence of the growth in complexity. Our findings suggest that the Industrial Revolution can be regarded as a sharp transition between different phases, but also imply that well developed economies can collapse if too many intermediate goods are introduced.Comment: 30 pages, 10 figure

The Ifo Industry Growth Accounting Database

In this paper we present a new database that allows deep industry-level growth accounting from 1991–2003. The database allows for the first complete analysis of the German industry performance drivers based on the contributions of 12 asset types in 52 different industries. The industry sources of productivity and output growth are crucial to the understanding of the transformation of the German economy from manufacturing to information technology and service industries. The database enables researchers to develop an adequate picture of the sources of growth using standard growth accounting techniques. We formally document the new data series and its origins, with special focus on the capital stock and capital service data.growth accounting, industry productivity analysis