Portfolio Margining: Strategy vs Risk

This paper presents the results of a novel mathematical and experimental analysis of two approaches to margining customer accounts, strategy-based and risk-based. Building combinatorial models of hedging mechanisms of these approaches, we show that the strategy-based approach is, at this point, the most appropriate one for margining security portfolios in customer margin accounts, while the risk-based approach can work efficiently for margining only index portfolios in customer mar-gin accounts and inventory portfolios of brokers. We also show that the application of the risk-based approach to security portfolios in customer margin accounts is very risky and can result in the pyramid of debt in the bullish market and the pyramid of loss in the bearish market. The results of this paper support the thesis that the use of the risk-based approach to margining customer accounts with positions in stocks and stock options since April 2007 influenced and triggered the U.S. stock market crash in October 2008. We also provide recommendations on ways to set appropriate margin requirements to help avoid such failures in the future

New Algorithms for Position Heaps

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and reduce the worst-case cost of insertions and deletions. Second, we show how to build a position heap in linear time independent of the size of the alphabet. Third, we show how to augment a position heap such that it supports access to the corresponding suffix array, and vice versa. Fourth, we introduce a variant of a position heap that can be simulated efficiently by a compressed suffix array with a linear number of extra bits

Gaussian limits for multidimensional random sequential packing at saturation (extended version)

Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $\lambda$ is asymptotically normal as $\lambda \to \infty$. We provide a rate of approximation to the normal and show that the finite dimensional distributions of the packing measures converge to those of a mean zero generalized Gaussian field. The method of proof involves showing that the collection of accepted solids satisfies the weak spatial dependence condition known as stabilization.Comment: 31 page

Drawing Graphs within Restricted Area

We study the problem of selecting a maximum-weight subgraph of a given graph such that the subgraph can be drawn within a prescribed drawing area subject to given non-uniform vertex sizes. We develop and analyze heuristics both for the general (undirected) case and for the use case of (directed) calculation graphs which are used to analyze the typical mistakes that high school students make when transforming mathematical expressions in the process of calculating, for example, sums of fractions

Modulation of systemic cytokine levels by implantation of alginate encapsulated cells

The availability of cell lines that are transfected with IL-4, IL-5 and IFN-γ cytokine genes permits the prolonged in vivo delivery of functional cytokines in relatively large doses for the modulation of specific immune responses. Oft

An Analogy between Bin Packing Problem and Permutation Problem: A New Encoding Scheme

Part 2: Knowledge Discovery and SharingInternational audienceThe bin packing problem aims to pack a set of items in a minimum number of bins, with respect to the size of the items and capacity of the bins. This is an NP-hard problem. Several approach methods have been developed to solve this problem. In this paper, we propose a new encoding scheme which is used in a hybrid resolution: a metaheuristic is matched with a list algorithm (Next Fit, First Fit, Best Fit) to solve the bin packing problem. Any metaheuristic can be used but in this paper, our proposition is implemented on a single solution based metaheuristic (stochastic descent, simulated annealing, kangaroo algorithm). This hybrid method is tested on literature instances to ensure its good results

Asymptotic Expansions for the Conditional Sojourn Time Distribution in the M/M/1M/M/1-PS Queue

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl

Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2

In this paper we study variants of the non-preemptive parallel job scheduling problem in which the number of machines is polynomially bounded in the number of jobs. For this problem we show that a schedule with length at most (1 + ε)OPT can be calculated in polynomial time. Unless P = NP, this is the best possible result (in the sense of approximation ratio), since the problem is strongly NP-hard. For the case, where all jobs must be allotted to a subset of consecutive machines, a schedule with length at most (1.5 + ε)OPT can be calculated in polynomial time. The previously best known results are algorithms with absolute approximation ratio 2. Furthermore, we extend both algorithms to the case of malleable jobs with the same approximation ratios

An Average-Case Analysis for Rate-Monotonic Multiprocessor Real-time Scheduling

We introduce the "First Fit Matching Periods" algorithm for static-priority multiprocessor scheduling of periodic tasks with implicit deadlines and show that it yields asymptotically optimal processor assignments if utilization values are chosen uniformly at random. More precisely we prove that the expected waste is upper bounded by O(n^(3/4) * (log n)^(3/8)). Here the waste denotes the ratio of idle times, cumulated over all processors and n gives the number of tasks. The algorithm can be implemented to run in time O(n log n) and even in the worst case, an asymptotic approximation ratio of 2 is guaranteed. Experiments yield an expected waste proportional to n^0.70, indicating that the above upper bound on the expected waste is almost tight