SIGSAM Bull.Pub Date : 2003-03-01DOI: 10.1145/844076.844084
M. Davison
{"title":"Review of risk management: value at risk and beyond, edited by M.A.H. Dempster. Cambridge University Press 2002.","authors":"M. Davison","doi":"10.1145/844076.844084","DOIUrl":"https://doi.org/10.1145/844076.844084","url":null,"abstract":"This book is a collection of nine papers presented at a Workshop on Risk Management held at the Isaac Newton Institute for Mathematical Sciences in October 1998. This suggests the risk that the book is a mélange of dated papers of strictly academic interest. Happily, nothing could be further from the truth. This book allows a reader equipped only with basic ideas of modern risk management to advance rapidly to the frontiers of research in this area. Perhaps because the editor has selected as authors a good mix of practitioners and academics, the book is useful to both groups of finance researchers. Value at Risk (VaR) quantifies the maximum amount, with probability x, that a portfolio can lose. That is, (1 − x) of the time one expects portfolio losses to exceed the VaR. The book opens with Picoult's paper \" Quantifying the Risk of Trading \" , which describes the fundamentals of VaR-based risk analysis. It focuses on valuation uncertainty, market risk, and counterparty credit risk. The final chapter of the book, Medova and Kyriacou's \" Extremes in Operational Risk Management \" , adds a mathematical framework for analyzing risks associated with human error or fraud, system breakdowns, or other external factors such as natural disasters. Three other contributions, of particular interest to the mathematician, describe modern modifications to and improvement of VaR, including the incorporation tail loss estimators, problems with correlations and their replacement by the copula technique, and extreme value statistics. Those thinking that innovations such as these make VaR obsolete are disabused of the notion by chapter 2, \" Value at Risk Analysis of a Leveraged Swap \" , by Sanjay Srivastava. This chapter described how application of basic VaR techniques could have kept Proctor & Gamble out of a spectacularly unsuccessful pair of interest rate swap trades. Kupiec contributes a chapter focusing on the important problem of \" Stress Testing in a Value at Risk Framework \". Stress testing is a way of exploring the effect of possible scenarios on an investment portfolio. The scenarios may be generated by looking at past financial market crises (such as that around the devaluation of the Thai Baht), either by assuming that past correlations between asset prices remain invariant or by introducing volatility and correlation shocks. Value at Risk presents many computational challenges. It is particularly difficult to determine the VaR of a large, complicated portfolio whose positions …","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116534929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2003-03-01DOI: 10.1145/844076.844080
R. Fateman
{"title":"Comparing the speed of programs for sparse polynomial multiplication","authors":"R. Fateman","doi":"10.1145/844076.844080","DOIUrl":"https://doi.org/10.1145/844076.844080","url":null,"abstract":"How should one design and implement a program for the multiplication of sparse polynomials? This is a simple question, necessarily addressed by the builders of any computer algebra system (CAS). To examine a few options we start with a single easily-stated computation which we believe represents a useful benchmark of \"medium difficulty\" for CAS designs. We describe a number of design options and their effects on performance. We also examine the performance of a variety of commercial and freely-distributed systems. Important considerations include the cost of high-precision (exact) integer arithmetic and the effective use of cache memory.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114876063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2002-12-01DOI: 10.1145/641239.641241
G. Cooperman, Xiaoqin Ma
{"title":"Overcoming the memory wall in symbolic algebra: a faster permutation multiplication","authors":"G. Cooperman, Xiaoqin Ma","doi":"10.1145/641239.641241","DOIUrl":"https://doi.org/10.1145/641239.641241","url":null,"abstract":"The traditional permutation multiplication algorithm is now limited by memory latency and not by CPU speed. A new cache-aware permutation algorithm speeds up permutation multiplication by a factor of 3.4 on current CPUs. The new algorithm is limited by memory bandwidth, but not by memory latency. Current trends indicate improving memory bandwidth and stagnant memory latency. This makes the new algorithm especially important for future computer architectures. In addition, we believe this \"memory wall\" will soon force a redesign of other common algorithms of symbolic algebra.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130775043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2002-12-01DOI: 10.1145/641239.641242
M. P. Barnett
{"title":"Computer algebra in the life sciences","authors":"M. P. Barnett","doi":"10.1145/641239.641242","DOIUrl":"https://doi.org/10.1145/641239.641242","url":null,"abstract":"This note (1) provides references to recent work that applies computer algebra (CA) to the life sciences, (2) cites literature that explains the biological background of each application, (3) states the mathematical methods that are used, (4) mentions the benefits of CA, and (5) suggests some topics for future work.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115750856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2002-09-04DOI: 10.1007/978-3-540-24616-9_10
Mohamed Shalaby, B. Jüttler, J. Schicho
{"title":"C1 spline implicitization of planar curves","authors":"Mohamed Shalaby, B. Jüttler, J. Schicho","doi":"10.1007/978-3-540-24616-9_10","DOIUrl":"https://doi.org/10.1007/978-3-540-24616-9_10","url":null,"abstract":"","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116457320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2002-09-01DOI: 10.1145/603273.603275
William Y. Sit
{"title":"East Coast Computer Algebra day: ECCAD 2002 poster and demonstration abstracts","authors":"William Y. Sit","doi":"10.1145/603273.603275","DOIUrl":"https://doi.org/10.1145/603273.603275","url":null,"abstract":"East Coast Computer Algebra Day 2002 (ECCAD 02) was held on May 18, 2002 at LaGuardia Community College of The City University of New York, New York. The abstracts of the invited speakers were published in the March 2002 issue of this Bulletin. Below are the abstracts of posters and demonstrations that were accepted and presented at the conference (some posters were presented in absentia).","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121734289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2002-09-01DOI: 10.1145/603273.603277
Tateaki Sasaki, Akira Terui
{"title":"A formula for separating small roots of a polynomial","authors":"Tateaki Sasaki, Akira Terui","doi":"10.1145/603273.603277","DOIUrl":"https://doi.org/10.1145/603273.603277","url":null,"abstract":"Let <i>P(x)</i> be a univariate polynomial over C, such that <i>P(x) = c<inf>n</inf>x<sup>n</sup> + ... + c<inf>m+1</inf>x<sup>m+1</sup> + x<sup>m</sup> + e<inf>m-1</inf>x<sup>m-1</sup> + ... + e<inf>0</inf>,</i> where max{<i>|c<inf>n</inf>|, ..., |c<inf>m+1</inf>|</i>} = 1 and <i>e</i> = max{<i>|e<inf>m-1</inf>|, |e<inf>m-2</inf>|<sup>1/2</sup>, ..., |e<inf>0</inf>|<sup>1/m</sup></i>} << 1. <i>P(x)</i> has <i>m</i> small roots around the origin so long as <i>e</i> << 1. In 1999, we derived a formula that if <i>e</i> < 1/9 then <i>P(x)</i> has <i>m</i> roots inside a disc <i>D</i><inf>in</inf> of radius <i>R</i><inf>in</inf> and other <i>n - m</i> roots outside a disc <i>D</i><inf>out</inf> of radius <i>R</i><inf>out</inf>, located at the origin, where <i>R</i><inf>in(out)</inf> = [1 - (+) √1 - (16<i>e</i>)/(1 + 3<i>e</i>)<sup>2</sup>] × (1 + 3<i>e</i>)/4. Note that <i>R</i><inf>in</inf> = <i>R</i><inf>out</inf> if <i>e</i> = 1/9. Our formula is essentially the same as that derived independently by Yakoubsohn at almost the same time. In this short article, we introduce the formula and check its sharpness on many polynomials generated randomly.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127233790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2002-06-02DOI: 10.1145/581316.581318
A. Franz, C. Schulzky, K. Hoffmann
{"title":"Using computer algebra methods to determine the chemical dimension of finitely ramified Sierpinski carpets","authors":"A. Franz, C. Schulzky, K. Hoffmann","doi":"10.1145/581316.581318","DOIUrl":"https://doi.org/10.1145/581316.581318","url":null,"abstract":"We present a new algorithm for calculating the chemical dimension <i>d</i><inf>1</inf> of finitely ramified Sierpinski carpets. Using an algorithm of Dijkstra, we compute iteratively, using <sc>Mathematica</sc>, the shortest paths through a carpet. The scaling exponent of the lengths of these shortest paths over the linear size of the carpet is <i>d</i><inf>min</inf> the minimum path dimension, which is related to the chemical dimension.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115778408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2002-06-02DOI: 10.1145/581316.581317
G. Reid, Chris Smith, J. Verschelde
{"title":"Geometric completion of differential systems using numeric-symbolic continuation","authors":"G. Reid, Chris Smith, J. Verschelde","doi":"10.1145/581316.581317","DOIUrl":"https://doi.org/10.1145/581316.581317","url":null,"abstract":"Symbolic algorithms using a finite number of exact differentiations and eliminations are able to reduce over and under-determined systems of polynomially nonlinear differential equations to involutive form. The output involutive form enables the identification of consistent initial values, and eases the application of exact or numerical integration methods.Motivated to avoid expression swell of pure symbolic approaches and with the desire to handle systems with approximate coefficients, we propose the use of homotopy continuation methods to perform the differential-elimination process on such non-square systems. Examples such as the classic index 3 Pendulum illustrate the new procedure. Our approach uses slicing by random linear subspaces to intersect its jet components in finitely many points. Generation of enough generic points enables irreducible jet components of the differential system to be interpolated.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114367374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIGSAM Bull.Pub Date : 2002-03-01DOI: 10.1145/565145.565149
Mhenni M. Benghorbal, Robert M Corless
{"title":"The nth derivative","authors":"Mhenni M. Benghorbal, Robert M Corless","doi":"10.1145/565145.565149","DOIUrl":"https://doi.org/10.1145/565145.565149","url":null,"abstract":"The following problem is one that many first year calculus students find quite difficult:Given a formula for a function <i>f</i> in a variable <i>x,</i> find a formula for its <i>n</i>th derivative.<b>Example 1.1:</b> [1, p. 229] If<i>f</i>(<i>x</i>) = <i>x<sup>m</sup>,</i> (1)then its <i>n</i>th derivative is<i>f</i><sup>(<i>n</i>)</sup> (<i>x</i>) = <i>m-<sup>n</sup>x<sup>m-n</sup>,</i> (2)where<i>m-<sup>n</sup> = m</i>(<i>m</i> - 1) (<i>m</i> - 2) ṡṡṡ (<i>m - n</i> + 1).The difficulties for students include, first, the discovery of a formula valid for all integers <i>n</i> and, second, the proof (for example, by induction) that the formula is correct. Can computer algebra systems do better?It is certain that Macsyma could (we remember commands for infinite Taylor series expansion of elementary functions, and that necessarily involves discovering a correct formula for the <i>n</i>th derivative of the input). Currently, Maple cannot---at least, not without help, just with one command, now that the Formal Power Series package in the share library is no longer supported.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124568802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}