{"product_id":"mathematical-methods-for-finance-tools-for-asset-and-risk-management-207-frank-j-fabozzi-series-9781118312636","title":"Mathematical Methods for Finance Tools for Asset","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAbout the Authors xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 1 Basic Concepts: Sets, Functions, and Variables 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 2\u003c\/p\u003e \u003cp\u003eSets and Set Operations 2\u003c\/p\u003e \u003cp\u003eDistances and Quantities 6\u003c\/p\u003e \u003cp\u003eFunctions 10\u003c\/p\u003e \u003cp\u003eVariables 10\u003c\/p\u003e \u003cp\u003eKey Points 11\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 2 Differential Calculus 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 14\u003c\/p\u003e \u003cp\u003eLimits 15\u003c\/p\u003e \u003cp\u003eContinuity 17\u003c\/p\u003e \u003cp\u003eTotal Variation 19\u003c\/p\u003e \u003cp\u003eThe Notion of Differentiation 19\u003c\/p\u003e \u003cp\u003eCommonly Used Rules for Computing Derivatives 21\u003c\/p\u003e \u003cp\u003eHigher-Order Derivatives 26\u003c\/p\u003e \u003cp\u003eTaylor Series Expansion 34\u003c\/p\u003e \u003cp\u003eCalculus in More Than One Variable 40\u003c\/p\u003e \u003cp\u003eKey Points 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 3 Integral Calculus 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 44\u003c\/p\u003e \u003cp\u003eRiemann Integrals 44\u003c\/p\u003e \u003cp\u003eLebesgue-Stieltjes Integrals 47\u003c\/p\u003e \u003cp\u003eIndefinite and Improper Integrals 48\u003c\/p\u003e \u003cp\u003eThe Fundamental Theorem of Calculus 51\u003c\/p\u003e \u003cp\u003eIntegral Transforms 52\u003c\/p\u003e \u003cp\u003eCalculus in More Than One Variable 57\u003c\/p\u003e \u003cp\u003eKey Points 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 4 Matrix Algebra 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 60\u003c\/p\u003e \u003cp\u003eVectors and Matrices Defined 61\u003c\/p\u003e \u003cp\u003eSquare Matrices 63\u003c\/p\u003e \u003cp\u003eDeterminants 66\u003c\/p\u003e \u003cp\u003eSystems of Linear Equations 68\u003c\/p\u003e \u003cp\u003eLinear Independence and Rank 69\u003c\/p\u003e \u003cp\u003eHankel Matrix 70\u003c\/p\u003e \u003cp\u003eVector and Matrix Operations 72\u003c\/p\u003e \u003cp\u003eFinance Application 78\u003c\/p\u003e \u003cp\u003eEigenvalues and Eigenvectors 81\u003c\/p\u003e \u003cp\u003eDiagonalization and Similarity 82\u003c\/p\u003e \u003cp\u003eSingular Value Decomposition 83\u003c\/p\u003e \u003cp\u003eKey Points 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 5 Probability: Basic Concepts 85\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 86\u003c\/p\u003e \u003cp\u003eRepresenting Uncertainty with Mathematics 87\u003c\/p\u003e \u003cp\u003eProbability in a Nutshell 89\u003c\/p\u003e \u003cp\u003eOutcomes and Events 91\u003c\/p\u003e \u003cp\u003eProbability 92\u003c\/p\u003e \u003cp\u003eMeasure 93\u003c\/p\u003e \u003cp\u003eRandom Variables 93\u003c\/p\u003e \u003cp\u003eIntegrals 94\u003c\/p\u003e \u003cp\u003eDistributions and Distribution Functions 96\u003c\/p\u003e \u003cp\u003eRandom Vectors 97\u003c\/p\u003e \u003cp\u003eStochastic Processes 100\u003c\/p\u003e \u003cp\u003eProbabilistic Representation of Financial Markets 102\u003c\/p\u003e \u003cp\u003eInformation Structures 103\u003c\/p\u003e \u003cp\u003eFiltration 104\u003c\/p\u003e \u003cp\u003eKey Points 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 6 Probability: Random Variables and Expectations 107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 109\u003c\/p\u003e \u003cp\u003eConditional Probability and Conditional Expectation 110\u003c\/p\u003e \u003cp\u003eMoments and Correlation 112\u003c\/p\u003e \u003cp\u003eCopula Functions 114\u003c\/p\u003e \u003cp\u003eSequences of Random Variables 116\u003c\/p\u003e \u003cp\u003eIndependent and Identically Distributed Sequences 117\u003c\/p\u003e \u003cp\u003eSum of Variables 118\u003c\/p\u003e \u003cp\u003eGaussian Variables 120\u003c\/p\u003e \u003cp\u003eAppproximating the Tails of a Probability Distribution: Cornish-Fisher Expansion and Hermite Polynomials 123\u003c\/p\u003e \u003cp\u003eThe Regression Function 129\u003c\/p\u003e \u003cp\u003eFat Tails and Stable Laws 131\u003c\/p\u003e \u003cp\u003eKey Points 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 7 Optimization 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 148\u003c\/p\u003e \u003cp\u003eMaxima and Minima 149\u003c\/p\u003e \u003cp\u003eLagrange Multipliers 151\u003c\/p\u003e \u003cp\u003eNumerical Algorithms 156\u003c\/p\u003e \u003cp\u003eCalculus of Variations and Optimal Control Theory 161\u003c\/p\u003e \u003cp\u003eStochastic Programming 163\u003c\/p\u003e \u003cp\u003eApplication to Bond Portfolio: Liability-Funding Strategies 164\u003c\/p\u003e \u003cp\u003eKey Points 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 8 Difference Equations 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 182\u003c\/p\u003e \u003cp\u003eThe Lag Operator L 183\u003c\/p\u003e \u003cp\u003eHomogeneous Difference Equations 183\u003c\/p\u003e \u003cp\u003eRecursive Calculation of Values of Difference Equations 192\u003c\/p\u003e \u003cp\u003eNonhomogeneous Difference Equations 195\u003c\/p\u003e \u003cp\u003eSystems of Linear Difference Equations 201\u003c\/p\u003e \u003cp\u003eSystems of Homogeneous Linear Difference Equations 202\u003c\/p\u003e \u003cp\u003eKey Points 209\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 9 Differential Equations 211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 212\u003c\/p\u003e \u003cp\u003eDifferential Equations Defined 213\u003c\/p\u003e \u003cp\u003eOrdinary Differential Equations 213\u003c\/p\u003e \u003cp\u003eSystems of Ordinary Differential Equations 216\u003c\/p\u003e \u003cp\u003eClosed-Form Solutions of Ordinary Differential Equations 218\u003c\/p\u003e \u003cp\u003eNumerical Solutions of Ordinary Differential Equations 222\u003c\/p\u003e \u003cp\u003eNonlinear Dynamics and Chaos 228\u003c\/p\u003e \u003cp\u003ePartial Differential Equations 231\u003c\/p\u003e \u003cp\u003eKey Points 237\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 10 Stochastic Integrals 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 240\u003c\/p\u003e \u003cp\u003eThe Intuition behind Stochastic Integrals 243\u003c\/p\u003e \u003cp\u003eBrownian Motion Defined 248\u003c\/p\u003e \u003cp\u003eProperties of Brownian Motion 254\u003c\/p\u003e \u003cp\u003eStochastic Integrals Defined 255\u003c\/p\u003e \u003cp\u003eSome Properties of Itoˆ Stochastic Integrals 259\u003c\/p\u003e \u003cp\u003eMartingale Measures and the Girsanov Theorem 260\u003c\/p\u003e \u003cp\u003eKey Points 266\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 11 Stochastic Differential Equations 267\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 268\u003c\/p\u003e \u003cp\u003eThe Intuition behind Stochastic Differential Equations 269\u003c\/p\u003e \u003cp\u003eItoˆ Processes 272\u003c\/p\u003e \u003cp\u003eStochastic Differential Equations 273\u003c\/p\u003e \u003cp\u003eGeneralization to Several Dimensions 276\u003c\/p\u003e \u003cp\u003eSolution of Stochastic Differential Equations 278\u003c\/p\u003e \u003cp\u003eDerivation of Itoˆ ’s Lemma 282\u003c\/p\u003e \u003cp\u003eDerivation of the Black-Scholes Option Pricing Formula 284\u003c\/p\u003e \u003cp\u003eKey Points 291\u003c\/p\u003e \u003cp\u003eIndex 293\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406850302295,"sku":"9781118312636","price":94.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118312636.jpg?v=1730497335","url":"https:\/\/bookcurl.com\/products\/mathematical-methods-for-finance-tools-for-asset-and-risk-management-207-frank-j-fabozzi-series-9781118312636","provider":"Book 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