LEADER 05759nam 2200769 450 001 9910139002903321 005 20200520144314.0 010 $a1-118-42149-3 010 $a1-118-65660-1 010 $a1-118-42008-X 035 $a(CKB)2550000001123281 035 $a(EBL)1378780 035 $a(SSID)ssj0000981885 035 $a(PQKBManifestationID)11985299 035 $a(PQKBTitleCode)TC0000981885 035 $a(PQKBWorkID)10982763 035 $a(PQKB)10101833 035 $a(DLC) 2013016582 035 $a(Au-PeEL)EBL1378780 035 $a(CaPaEBR)ebr10768964 035 $a(CaONFJC)MIL522017 035 $a(CaSebORM)9781118421499 035 $a(MiAaPQ)EBC1378780 035 $a(OCoLC)841199228 035 $a(PPN)179864505 035 $a(EXLCZ)992550000001123281 100 $a20130412h20132013 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical methods for finance $etools for asset and risk management /$fSergio M. Focardi, Frank J. Fabozzi, Turan G. Bali 205 $a1st edition 210 1$aHoboken, New Jersey :$cJohn Wiley & Sons, Inc.,$d[2013] 210 4$dİ2013 215 $a1 online resource (322 p.) 225 1 $aThe Frank J. Fabozzi series 300 $aIncludes index. 311 $a1-118-31263-5 311 $a1-299-90766-0 320 $aIncludes bibliographical references and index. 327 $aMathematical Methods for Finance; Contents; Preface; About the Authors; CHAPTER 1 Basic Concepts: Sets, Functions, and Variables; INTRODUCTION; SETS AND SET OPERATIONS; Proper Subsets; Empty Sets; Union of Sets; Intersection of Sets; Elementary Properties of Sets; DISTANCES AND QUANTITIES; n-tuples; Distance; Density of Points; FUNCTIONS; VARIABLES; KEY POINTS; CHAPTER 2 Differential Calculus; INTRODUCTION; LIMITS; CONTINUITY; TOTAL VARIATION; THE NOTION OF DIFFERENTIATION; COMMONLY USED RULES FOR COMPUTING DERIVATIVES; HIGHER-ORDER DERIVATIVES; Application to Bond Analysis 327 $aApplication of the Chain RuleTAYLOR SERIES EXPANSION; Application to Bond Analysis; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 3 Integral Calculus; INTRODUCTION; RIEMANN INTEGRALS; Properties of Riemann Integrals; LEBESGUE-STIELTJES INTEGRALS; INDEFINITE AND IMPROPER INTEGRALS; THE FUNDAMENTAL THEOREM OF CALCULUS; INTEGRAL TRANSFORMS; Laplace Transforms; Fourier Transforms; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 4 Matrix Algebra; INTRODUCTION; VECTORS AND MATRICES DEFINED; Vectors; Matrices; SQUARE MATRICES; Diagonals and Antidiagonals; Identity Matrix 327 $aDiagonal MatrixUpper and Lower Triangular Matrix; DETERMINANTS; SYSTEMS OF LINEAR EQUATIONS; LINEAR INDEPENDENCE AND RANK; HANKEL MATRIX; VECTOR AND MATRIX OPERATIONS; Vector Operations; Matrix Operations; FINANCE APPLICATION; EIGENVALUES AND EIGENVECTORS; DIAGONALIZATION AND SIMILARITY; SINGULAR VALUE DECOMPOSITION; KEY POINTS; CHAPTER 5 Probability: Basic Concepts; INTRODUCTION; REPRESENTING UNCERTAINTY WITH MATHEMATICS; PROBABILITY IN A NUTSHELL; OUTCOMES AND EVENTS; PROBABILITY; MEASURE; RANDOM VARIABLES; INTEGRALS; DISTRIBUTIONS AND DISTRIBUTION FUNCTIONS; RANDOM VECTORS 327 $aSTOCHASTIC PROCESSESPROBABILISTIC REPRESENTATION OF FINANCIAL MARKETS; INFORMATION STRUCTURES; FILTRATION; KEY POINTS; CHAPTER 6 Probability: Random Variables and Expectations; INTRODUCTION; CONDITIONAL PROBABILITY AND CONDITIONAL EXPECTATION; MOMENTS AND CORRELATION; COPULA FUNCTIONS; SEQUENCES OF RANDOM VARIABLES; INDEPENDENT AND IDENTICALLY DISTRIBUTED SEQUENCES; SUM OF VARIABLES; GAUSSIAN VARIABLES; APPROXIMATING THE TAILS OF A PROBABILITY DISTRIBUTION: CORNISH-FISHER EXPANSION AND HERMITE POLYNOMIALS; Cornish-Fisher Expansion; Hermite Polynomials 327 $aCornish-Fisher Expansion with Hermite PolynomialsTHE REGRESSION FUNCTION; Linear Regression; FAT TAILS AND STABLE LAWS; Fat Tails; The Class L of Fat-Tailed Distributions; The Law of Large Numbers and the Central Limit Theorem; Stable Distributions; KEY POINTS; CHAPTER 7 Optimization; INTRODUCTION; MAXIMA AND MINIMA; LAGRANGE MULTIPLIERS; NUMERICAL ALGORITHMS; Linear Programming; Quadratic Programming; CALCULUS OF VARIATIONS AND OPTIMAL CONTROL THEORY; STOCHASTIC PROGRAMMING; APPLICATION TO BOND PORTFOLIO: LIABILITY-FUNDING STRATEGIES; Cash Flow Matching; Portfolio Immunization 327 $aScenario Optimization 330 $aThe mathematical and statistical tools needed in the rapidly growing quantitative finance field With the rapid growth in quantitative finance, practitioners must achieve a high level of proficiency in math and statistics. Mathematical Methods and Statistical Tools for Finance, part of the Frank J. Fabozzi Series, has been created with this in mind. Designed to provide the tools needed to apply finance theory to real world financial markets, this book offers a wealth of insights and guidance in practical applications. It contains applications that are broader in scope from wha 410 0$aFrank J. Fabozzi series. 606 $aFinance$xMathematical models 606 $aAsset-liability management$xMathematical models 606 $aRisk management$xMathematical models 615 0$aFinance$xMathematical models. 615 0$aAsset-liability management$xMathematical models. 615 0$aRisk management$xMathematical models. 676 $a332.01/5195 700 $aFocardi$b Sergio M$03962 701 $aFabozzi$b Frank J$0109596 701 $aBali$b Turan G$0860243 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139002903321 996 $aMathematical methods for finance$91919468 997 $aUNINA