E0 370 Statistical Learning Theory Lecture 20 (Nov 17, 2011)


 Lorraine James
 2 years ago
 Views:
Transcription
1 E0 370 Saisical Learning Theory Lecure 0 (ov 7, 0 Online Learning from Expers: Weighed Majoriy and Hedge Lecurer: Shivani Agarwal Scribe: Saradha R Inroducion In his lecure, we will look a he problem of learning from muliple expers in an online fashion. There are finie number of expers, who give heir predicions ξ,..., ξ. The learning algorihm has o use he predicor values and come up wih an oucome ŷ. The oal number of misakes made by he algorihm is compared wih he performance of he bes exper in consideraion. Online Predicion from Expers A general online predicion problem proceeds as follows. Online (binary predicion using muliple expers For =,..., T : Receive exper predicors ξ (x,..., ξ (x {±} Predic ŷ {±} Receive rue label y {±} Incur loss l(y, ŷ. Halving Algorihm Here we assume ha he se of expers ha we consider has an exper which would give he correc label for all insances. In he halving algorihm, for every ieraion, only he consisen expers are reained. If a predicor makes a misake i will no more be conribuing in he predicion process. Halving Algorihm Iniiae weighs wi = i ] For =,..., T : Receive exper predicors ξ (x,..., ξ (x {±} Predic ŷ = sign( n j= w j.ξ j (majoriy voe Receive rue label y {±} Incur loss l(y, ŷ Updae: Updae: i... : Ifξi y hen i 0 else i wi
2 Online Learning from Expers: Weighed Majoriy and Hedge Thus he maximum number of misakes, or he sum of loss over any given sequence is bounded by he logarihm of number of predicors. i.e. L 0 S Halving] log.. Weighed Majoriy (WM Algorihm In he halving algorihm, when a predicor makes even one misake, i will no be able o conribue o he predicion in he successive ieraions. When we don have an exper ha would predic correcly for all samples, his would no be a suiable approach. The weighed majoriy algorihm works well in such siuaions. Here every predicor is assigned equal weigh, say, iniially. Laer as hey make binary predicions on insances, he weighs of he predicors are decreased using muliplicaive updae, when hey commi misakes. The rae a which he weighs are updaed is governed by he parameer. Weighed majoriy Algorihm Iniiae weighs wi = i ] For =,..., T : Receive exper predicors ξ (x,..., ξ (x {±} Predic ŷ = sign( n j= w j.ξ j Receive rue label y {±} Incur loss l(y, ŷ Updae: If ŷ y i... i w i exp(.i(y ξ i (majoriy voe Theorem.. Le ξ,..., ξ {±} T. Le S = (y,..., y T {±} and le > 0. Then he oal number of misakes ( L 0 S W eighedm ajoriy(] +exp(. min L 0 S ξ i ] + i. +exp(. Proof. Denoe L 0 S W eighedmajoriy] = L For each rial on which here is a misake, we have + = wi. exp (.I(y ξ i. ( = w i. exp + w i ( i:y ξ i i:y =ξ i = exp.w maj + W min (3 For all misake rials, we have + Therefore summing over =,..., T gives exp.w maj + W min + exp (W maj W min (4 = + exp.(w maj + W min +exp. For oher rials, + W W T + W T = + exp.( (5 ( + exp L. (6
3 Online Learning from Expers: Weighed Majoriy and Hedge 3 L ln W ln W T + +exp (. (7 Finding he lower bound on ln W T + + = j= w T + j w T + j exp.li w i ( i. (8 L ln W.L i ln wi +e ( = ln +.L i +e ( (9 (0 for all w j > 0 j Thus we obain he resul..3 Weighed Majoriy: Coninuous Version (WMC We now see he coninuous version of weighed majoriy algorihm. The final predicion is a weighed average of he exper predicor values. Here ỹ = ŷ = y = 0, ] Weighed majoriy Algorihm :Coninuous Version (WMC Iniiae weighs wi = i ] For =,..., T : Receive exper predicors ξ (x,..., ξ (x 0, ] Predic ŷ = w i.ξ i 0, ] (Weighed Average w i Receive rue label y 0, ] Incur loss l abs (y, ŷ = y ŷ Updae: i... i wi. exp. ξ i y Theorem.. Le ξ,..., ξ 0, ] T. Le S = (y,..., y T 0, ] and le > 0. Then he oal number of misakes S W MC(] (. min exp i L abs L abs S ξ i ] +.. exp Proof. Denoe L abs S W MC(] = L For each rial we have + = wi. exp. y ξ i. ( wi. ( exp y ξi ]. (
4 4 Online Learning from Expers: Weighed Majoriy and Hedge + wi ( exp w i y ξi (3 w i. ( exp w i y ξi (4 w i =. ( exp ŷ y ] (5 ] +. exp ( exp. ŷ y. (6 + exp ( exp. T = ŷ y ] = exp ( exp.l exp ( exp. ŷ y ] (7 (8 Finding he lower bound on ln W T + L ln W ln W T + (exp. (9 + exp.li w i ( i. (0 Thus we obain he resul L ln W T + +.L i ln wi (exp ( ln +.L i (exp. ( 3 Online Allocaion The problem of online allocaion occurs in scenarios where we need o allocae differen fracion of resources ino differen opions. The loss associaed wih every opion is available a he end of every ieraion. We would like o reduce he oal loss suffered for he paricular allocaion. The allocaion for he nex ieraion is hen revised, based on he oal loss suffered in he curren ieraion using muliplicaive updae. Hedge Algorihm( Iniiae weighs wi = i ] For =,..., T : Make allocaion p p = w ; w i Receive vecor of loses l = (l,..., l 0, ] Incur loss p.l = p i.l i Updae: i... i wi. exp (l i
5 Online Learning from Expers: Weighed Majoriy and Hedge 5 Theorem 3.. Le l,..., l T 0, ] The cumulaive loss of he algorihm is LA] = T p.l If he loss of a paricular opion over he T ieraions is given by Then L T l i. LHedge(] (. min L exp i +.. i exp Proof. Denoe LHedge(] = L For each rial we have + = wi. exp.l i. (3 wi. ( exp. w i.l i. (4 w i + wi ( exp p.l ]. (5 + exp ( exp.p.l ] (6 ] exp ( exp.l (7 L ln W ln W T + (exp. (8 Finding he lower bound on ln W T + + exp.li w i ( i. (9 Thus we obain he resul L ln W T + +.L i ln wi (exp (30 ln +.L i (exp. (3 4 ex Lecure In he nex lecure, we will inroduce he idea of minimax regre, in an adversarial learning seing. References
MTH6121 Introduction to Mathematical Finance Lesson 5
26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random
More informationMarkov Models and Hidden Markov Models (HMMs)
Markov Models and Hidden Markov Models (HMMs (Following slides are modified from Prof. Claire Cardie s slides and Prof. Raymond Mooney s slides. Some of he graphs are aken from he exbook. Markov Model
More informationI. Basic Concepts (Ch. 14)
(Ch. 14) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing
More informationTask is a schedulable entity, i.e., a thread
RealTime Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T:  s: saring poin  e: processing ime of T  d: deadline of T  p: period of T Periodic ask T
More informationMultiobjective Prediction with Expert Advice
Muliobjecive Predicion wih Exper Advice Alexey Chernov Compuer Learning Research Cenre and Deparmen of Compuer Science Royal Holloway Universiy of London GTP Workshop, June 2010 Alexey Chernov (RHUL) Muliobjecive
More informationNewton's second law in action
Newon's second law in acion In many cases, he naure of he force acing on a body is known I migh depend on ime, posiion, velociy, or some combinaion of hese, bu is dependence is known from experimen In
More informationParameterFree Convex Learning through Coin Betting
JMLR: Workshop and Conference Proceedings 1:1 7, 2016 ICML 2016 AuoML Workshop ParameerFree Convex Learning hrough Coin Being Francesco Orabona Dávid Pál Yahoo Research, New York FRANCESCO@ORABONA.COM
More informationSinglemachine Scheduling with Periodic Maintenance and both Preemptive and. Nonpreemptive jobs in Remanufacturing System 1
Absrac number: 050407 Singlemachine Scheduling wih Periodic Mainenance and boh Preempive and Nonpreempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy
More informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationLearning Eigenvectors for Free
Learning Eigenvecors for Free Wouer M Koolen Royal Holloway and CWI wouer@csrhulacuk Wojek Kołowski Cenrum Wiskunde & Informaica kolowsk@cwinl Manfred K Warmuh UC Sana Cruz manfred@cseucscedu Absrac We
More informationRenewal processes and Poisson process
CHAPTER 3 Renewal processes and Poisson process 31 Definiion of renewal processes and limi heorems Le ξ 1, ξ 2, be independen and idenically disribued random variables wih P[ξ k > 0] = 1 Define heir parial
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces imeseries smoohing forecasing mehods. Various models are discussed,
More informationAn Online Learningbased Framework for Tracking
An Online Learningbased Framework for Tracking Kamalika Chaudhuri Compuer Science and Engineering Universiy of California, San Diego La Jolla, CA 9293 Yoav Freund Compuer Science and Engineering Universiy
More informationGLAS Team Member Quarterly Report. June , Golden, Colorado (Colorado School of Mines)
GLAS Team ember Quarerly Repor An Nguyen, Thomas A Herring assachuses Insiue of Technology Period: 04/01/2004 o 06/30//2004 eeings aended Tom Herring aended he eam meeing near GSFC a he end of June, 2004.
More informationSPEC model selection algorithm for ARCH models: an options pricing evaluation framework
Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,
More informationGraphing the Von Bertalanffy Growth Equation
file: d:\b1732013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and
More informationThe Application of Multi Shifts and Break Windows in Employees Scheduling
The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchangeraded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationAn empirical analysis about forecasting Tmall airconditioning sales using time series model Yan Xia
An empirical analysis abou forecasing Tmall aircondiioning sales using ime series model Yan Xia Deparmen of Mahemaics, Ocean Universiy of China, China Absrac Time series model is a hospo in he research
More informationTable of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
More informationA Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)
A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke
More informationSupply Chain Management Using Simulation Optimization By Miheer Kulkarni
Supply Chain Managemen Using Simulaion Opimizaion By Miheer Kulkarni This problem was inspired by he paper by Jung, Blau, Pekny, Reklaii and Eversdyk which deals wih supply chain managemen for he chemical
More informationMath 201 Lecture 12: CauchyEuler Equations
Mah 20 Lecure 2: CauchyEuler Equaions Feb., 202 Many examples here are aken from he exbook. The firs number in () refers o he problem number in he UA Cusom ediion, he second number in () refers o he problem
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More information4 Convolution. Recommended Problems. x2[n] 1 2[n]
4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discreeime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.11.
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More information1 The basic circulation problem
2WO08: Graphs and Algorihms Lecure 4 Dae: 26/2/2012 Insrucor: Nikhil Bansal The Circulaion Problem Scribe: Tom Slenders 1 The basic circulaion problem We will consider he maxflow problem again, bu his
More informationTSGRAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999
TSGRAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macrodiversiy for he PRACH Discussion/Decision
More information4. The Poisson Distribution
Virual Laboraories > 13. The Poisson Process > 1 2 3 4 5 6 7 4. The Poisson Disribuion The Probabiliy Densiy Funcion We have shown ha he k h arrival ime in he Poisson process has he gamma probabiliy densiy
More informationON THURSTONE'S MODEL FOR PAIRED COMPARISONS AND RANKING DATA
ON THUSTONE'S MODEL FO PAIED COMPAISONS AND ANKING DATA Alber MaydeuOlivares Dep. of Psychology. Universiy of Barcelona. Paseo Valle de Hebrón, 171. 08035 Barcelona (Spain). Summary. We invesigae by means
More informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4112008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More informationDensity Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n).
FW 662 Densiydependen populaion models In he previous lecure we considered densiy independen populaion models ha assumed ha birh and deah raes were consan and no a funcion of populaion size. Longerm
More informationA Short Introduction to Boosting
Journal of Japanese Sociey for Arificial Inelligence,14(5):771780, Sepember, 1999. (In Japanese, ranslaion by Naoki Abe.) A Shor Inroducion o Boosing Yoav Freund Rober E. Schapire AT&T Labs Research Shannon
More informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a missiondriven noforprofi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More informationA dynamic probabilistic modeling of railway switches operating states
A dynamic probabilisic modeling of railway swiches operaing saes Faicel Chamroukhi 1, Allou Samé 1, Parice Aknin 1, Marc Anoni 2 1 IFSTTAR, 2 rue de la Bue Vere, 93166 NoisyleGrand Cedex, France {chamroukhi,same,aknin}@ifsar.fr
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationRevisions to Nonfarm Payroll Employment: 1964 to 2011
Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm
More informationSuggested Reading. Signals and Systems 42
4 Convoluion In Lecure 3 we inroduced and defined a variey of sysem properies o which we will make frequen reference hroughou he course. Of paricular imporance are he properies of lineariy and ime invariance,
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationLecture 18. Serial correlation: testing and estimation. Testing for serial correlation
Lecure 8. Serial correlaion: esing and esimaion Tesing for serial correlaion In lecure 6 we used graphical mehods o look for serial/auocorrelaion in he random error erm u. Because we canno observe he u
More informationA NOTE ON UNIT SYSTEMS
Tom Aage Jelmer NTNU eparmen of Peroleum Engineering and Applied Geophysics Inroducory remarks A NOTE ON UNIT SYSTEMS So far, all equaions have been expressed in a consisen uni sysem. The SI uni sysem
More informationLongevity 11 Lyon 79 September 2015
Longeviy 11 Lyon 79 Sepember 2015 RISK SHARING IN LIFE INSURANCE AND PENSIONS wihin and across generaions Ragnar Norberg ISFA Universié Lyon 1/London School of Economics Email: ragnar.norberg@univlyon1.fr
More informationCommunication Networks II Contents
3 / 1  Communicaion Neworks II (Görg)  www.comnes.unibremen.de Communicaion Neworks II Conens 1 Fundamenals of probabiliy heory 2 Traffic in communicaion neworks 3 Sochasic & Markovian Processes (SP
More informationA NOTE ON THE ALMOST EVERYWHERE CONVERGENCE OF ALTERNATING SEQUENCES WITH DUNFORD SCHWARTZ OPERATORS
C O L L O Q U I U M M A T H E M A T I C U M VOL. LXII 1991 FASC. I A OTE O THE ALMOST EVERYWHERE COVERGECE OF ALTERATIG SEQUECES WITH DUFORD SCHWARTZ OPERATORS BY RYOTARO S A T O (OKAYAMA) 1. Inroducion.
More informationSmall and Large Trades Around Earnings Announcements: Does Trading Behavior Explain PostEarningsAnnouncement Drift?
Small and Large Trades Around Earnings Announcemens: Does Trading Behavior Explain PosEarningsAnnouncemen Drif? Devin Shanhikumar * Firs Draf: Ocober, 2002 This Version: Augus 19, 2004 Absrac This paper
More informationINDEPENDENT MARGINALS OF OPERATOR LÉVY S PROBABILITY MEASURES ON FINITE DIMENSIONAL VECTOR SPACES
Journal of Applied Analysis 1, 1 (1995), pp. 39 45 INDEPENDENT MARGINALS OF OPERATOR LÉVY S PROBABILITY MEASURES ON FINITE DIMENSIONAL VECTOR SPACES A. LUCZAK Absrac. We find exponens of independen marginals
More informationFair games, and the Martingale (or "Random walk") model of stock prices
Economics 236 Spring 2000 Professor Craine Problem Se 2: Fair games, and he Maringale (or "Random walk") model of sock prices Sephen F LeRoy, 989. Efficien Capial Markes and Maringales, J of Economic Lieraure,27,
More informationEconomics 140A Hypothesis Testing in Regression Models
Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1
More informationPredicting Stock Market Index Trading Signals Using Neural Networks
Predicing Sock Marke Index Trading Using Neural Neworks C. D. Tilakarane, S. A. Morris, M. A. Mammadov, C. P. Hurs Cenre for Informaics and Applied Opimizaion School of Informaion Technology and Mahemaical
More informationWorking Paper Social security systems, human capital, and growth in a small open economy
econsor www.econsor.eu Der OpenAccessPublikaionsserver der ZBW LeibnizInformaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Kaganovich, Michael;
More informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationState Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University
Inroducion ae Machines: Brief Inroducion o equencers Prof. Andrew J. Mason, Michigan ae Universiy A sae machine models behavior defined by a finie number of saes (unique configuraions), ransiions beween
More informationTechnical Appendix to Risk, Return, and Dividends
Technical Appendix o Risk, Reurn, and Dividends Andrew Ang Columbia Universiy and NBER Jun Liu UC San Diego This Version: 28 Augus, 2006 Columbia Business School, 3022 Broadway 805 Uris, New York NY 10027,
More informationEvolutionary building of stock trading experts in realtime systems
Evoluionary building of sock rading expers in realime sysems Jerzy J. Korczak Universié Louis Paseur Srasbourg, France Email: jjk@dpinfo.usrasbg.fr Absrac: This paper addresses he problem of consrucing
More informationTime Consistency in Portfolio Management
1 Time Consisency in Porfolio Managemen Traian A Pirvu Deparmen of Mahemaics and Saisics McMaser Universiy Torono, June 2010 The alk is based on join work wih Ivar Ekeland Time Consisency in Porfolio Managemen
More informationImproper Integrals. Dr. Philippe B. laval Kennesaw State University. September 19, 2005. f (x) dx over a finite interval [a, b].
Improper Inegrls Dr. Philippe B. lvl Kennesw Se Universiy Sepember 9, 25 Absrc Noes on improper inegrls. Improper Inegrls. Inroducion In Clculus II, sudens defined he inegrl f (x) over finie inervl [,
More informationMarkit Excess Return Credit Indices Guide for price based indices
Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semiannual
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More information= r t dt + σ S,t db S t (19.1) with interest rates given by a mean reverting OrnsteinUhlenbeck or Vasicek process,
Chaper 19 The BlackScholesVasicek Model The BlackScholesVasicek model is given by a sandard imedependen BlackScholes model for he sock price process S, wih imedependen bu deerminisic volailiy σ
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationAP Calculus AB 2007 Scoring Guidelines
AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and
More informationOn Stochastic and Worstcase Models for Investing
On Sochasic and Worscase Models for Invesing Elad Hazan IBM Almaden Research Cener 650 Harry Rd, San Jose, CA 9520 ehazan@cs.princeon.edu Sayen Kale Yahoo! Research 430 Grea America Parkway, Sana Clara,
More informationA Generalized Bivariate OrnsteinUhlenbeck Model for Financial Assets
A Generalized Bivariae OrnseinUhlenbeck Model for Financial Asses Romy Krämer, Mahias Richer Technische Universiä Chemniz, Fakulä für Mahemaik, 917 Chemniz, Germany Absrac In his paper, we sudy mahemaical
More informationPermutations and Combinations
Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes  ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he kvalue for he middle erm, divide
More informationOn the degrees of irreducible factors of higher order Bernoulli polynomials
ACTA ARITHMETICA LXII.4 (1992 On he degrees of irreducible facors of higher order Bernoulli polynomials by Arnold Adelberg (Grinnell, Ia. 1. Inroducion. In his paper, we generalize he curren resuls on
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationValuation of Life Insurance Contracts with Simulated Guaranteed Interest Rate
Valuaion of Life Insurance Conracs wih Simulaed uaraneed Ineres Rae Xia uo and ao Wang Deparmen of Mahemaics Royal Insiue of echnology 100 44 Sockholm Acknowledgmens During he progress of he work on his
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More informationExample: scheduling using EDF
EDA/DIT6 RealTime Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 RealTime Sysems Specificaion Implemenaion Dynamic scheduling  Earliesdeadlinefirs scheduling Processordemand analysis Verificaion
More informationNewton s Laws of Motion
Newon s Laws of Moion MS4414 Theoreical Mechanics Firs Law velociy. In he absence of exernal forces, a body moves in a sraigh line wih consan F = 0 = v = cons. Khan Academy Newon I. Second Law body. The
More informationRealtime Particle Filters
Realime Paricle Filers Cody Kwok Dieer Fox Marina Meilă Dep. of Compuer Science & Engineering, Dep. of Saisics Universiy of Washingon Seale, WA 9895 ckwok,fox @cs.washingon.edu, mmp@sa.washingon.edu Absrac
More informationOption Trading Costs Are Lower Than You Think
Opion Trading Coss Are Lower Than You Think Dmiriy Muravyev Boson College Neil D. Pearson Universiy of Illinois a UrbanaChampaign March 15, 2015 Absrac Convenionally measured bidask spreads of liquid
More informationnonlocal conditions.
ISSN 17493889 prin, 17493897 online Inernaional Journal of Nonlinear Science Vol.11211 No.1,pp.39 Boundary Value Problem for Some Fracional Inegrodifferenial Equaions wih Nonlocal Condiions Mohammed
More informationUsefulness of the Forward Curve in Forecasting Oil Prices
Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,
More informationINVESTMENT GUARANTEES IN UNITLINKED LIFE INSURANCE PRODUCTS: COMPARING COST AND PERFORMANCE
INVESMEN UARANEES IN UNILINKED LIFE INSURANCE PRODUCS: COMPARIN COS AND PERFORMANCE NADINE AZER HAO SCHMEISER WORKIN PAPERS ON RISK MANAEMEN AND INSURANCE NO. 4 EDIED BY HAO SCHMEISER CHAIR FOR RISK MANAEMEN
More informationImagine a Source (S) of sound waves that emits waves having frequency f and therefore
heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing
More informationStock Trading with Recurrent Reinforcement Learning (RRL) CS229 Application Project Gabriel Molina, SUID 5055783
Sock raing wih Recurren Reinforcemen Learning (RRL) CS9 Applicaion Projec Gabriel Molina, SUID 555783 I. INRODUCION One relaively new approach o financial raing is o use machine learning algorihms o preic
More informationForecasting, Ordering and Stock Holding for Erratic Demand
ISF 2002 23 rd o 26 h June 2002 Forecasing, Ordering and Sock Holding for Erraic Demand Andrew Eaves Lancaser Universiy / Andalus Soluions Limied Inroducion Erraic and slowmoving demand Demand classificaion
More informationFIN 472 FixedIncome Securities Approximating Price Changes: From Duration to Convexity Professor Robert B.H. Hauswald Kogod School of Business, AU
FIN 47 FixedIncome Securiies Approximaing rice Changes: From Duraion o Convexiy rofessor Rober B.H. Hauswald Kogod School of Business, AU Bond rice Volailiy Consider only IR as a risk facor Longer M means
More informationDynamic programming models and algorithms for the mutual fund cash balance problem
Submied o Managemen Science manuscrip Dynamic programming models and algorihms for he muual fund cash balance problem Juliana Nascimeno Deparmen of Operaions Research and Financial Engineering, Princeon
More informationOnline Algorithms: Learning & Optimization with No Regret.
Online Algorithms: Learning & Optimization with No Regret. Daniel Golovin 1 The Setup Optimization: Model the problem (objective, constraints) Pick best decision from a feasible set. Learning: Model the
More informationBayesian Inference of Arrival Rate and Substitution Behavior from Sales Transaction Data with Stockouts
Bayesian Inference of Arrival Rae and Subsiuion Behavior from Sales Transacion Daa wih Sockous Benjamin Leham 1, Lydia M. Leham, and Cynhia Rudin 3 1 Operaions Research Cener, Massachuses Insiue of Technology,
More informationTerm Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationMultiprocessor SystemsonChips
Par of: Muliprocessor SysemsonChips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,
More informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More informationTHE PRESSURE DERIVATIVE
Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics THE PRESSURE DERIVATIVE The ressure derivaive has imoran diagnosic roeries. I is also imoran for making ye curve analysis more reliable.
More informationOn the Connection Between MultipleUnicast Network Coding and SingleSource SingleSink Network Error Correction
On he Connecion Beween MulipleUnica ework Coding and SingleSource SingleSink ework Error Correcion Jörg Kliewer JIT Join work wih Wenao Huang and Michael Langberg ework Error Correcion Problem: Adverary
More informationAn Analysis of Tax Revenue Forecast Errors
An Analysis of Tax Revenue Forecas Errors Marin Keene and Peer Thomson N EW Z EALAND T REASURY W ORKING P APER 07/02 M ARCH 2007 NZ TREASURY WORKING PAPER 07/02 An Analysis of Tax Revenue Forecas Errors
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationA Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities *
A Universal Pricing Framework for Guaraneed Minimum Benefis in Variable Annuiies * Daniel Bauer Deparmen of Risk Managemen and Insurance, Georgia Sae Universiy 35 Broad Sree, Alana, GA 333, USA Phone:
More informationDependent Interest and Transition Rates in Life Insurance
Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies
More informationDifferential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.
Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given
More informationReal Time Bid Optimization with Smooth Budget Delivery in Online Advertising
Real Time Bid Opimizaion wih Smooh Budge Delivery in Online Adverising KuangChih Lee Ali Jalali Ali Dasdan Turn Inc. 835 Main Sree, Redwood Ciy, CA 94063 {klee,ajalali,adasdan}@urn.com ABSTRACT Today,
More informationModeling a distribution of mortgage credit losses Petr Gapko 1, Martin Šmíd 2
Modeling a disribuion of morgage credi losses Per Gapko 1, Marin Šmíd 2 1 Inroducion Absrac. One of he bigges risks arising from financial operaions is he risk of counerpary defaul, commonly known as a
More informationMODEL AND ALGORITHMS FOR THE REAL TIME MANAGEMENT OF RESIDENTIAL ELECTRICITY DEMAND. A. Barbato, G. Carpentieri
MODEL AND ALGORITHMS FOR THE REAL TIME MANAGEMENT OF RESIDENTIAL ELECTRICITY DEMAND A. Barbao, G. Carpenieri Poliecnico di Milano, Diparimeno di Eleronica e Informazione, Email: barbao@ele.polimi.i, giuseppe.carpenieri@mail.polimi.i
More information2.4 Network flows. Many direct and indirect applications telecommunication transportation (public, freight, railway, air, ) logistics
.4 Nework flow Problem involving he diribuion of a given produc (e.g., waer, ga, daa, ) from a e of producion locaion o a e of uer o a o opimize a given objecive funcion (e.g., amoun of produc, co,...).
More informationStrategic Optimization of a Transportation Distribution Network
Sraegic Opimizaion of a Transporaion Disribuion Nework K. John Sophabmixay, Sco J. Mason, Manuel D. Rossei Deparmen of Indusrial Engineering Universiy of Arkansas 4207 Bell Engineering Cener Fayeeville,
More information