金融中的数值方法和优化
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作者吉利 (M.Gilli) 著
出版社世界图书出版公司
ISBN9787510052651
出版时间2013-01
版次1
装帧平装
开本16开
纸张胶版纸
页数584页
定价89元
上书时间2024-08-01
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基本信息
书名:金融中的数值方法和优化
定价：89.00元
作者:吉利 (M.Gilli) 著
出版社：世界图书出版公司
出版日期：2013-01-01
ISBN：9787510052651
字数：
页码：584
版次：1
装帧：平装
开本：24开
商品重量：
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内容提要
《金融中的数值方法和优化(英文)》旨在为读者介绍金融计算工具—基本数值分析和计算技巧，如期权定价、并突出了模拟和优化的重要性，用许多章讲述投资组合保险和风险估计问题。特别地，有几章用于讲述优化探索和如何将他们应用于投资组合的选择、估值的校准和期权定价模型。这些具体的例子让读者学习了解决问题的具体步骤，以及将这些步骤举一反三。同时，这些应用使得《金融中的数值方法和优化(英文)》的参考价值大大提高。
目录
List of AlgorithmsAcknowledgements1.Introductio1.1 About thiook1.2 Principles1.3 on software1.4 on appromations andaccuracy1.5 Summary: the theme of the bookPart One Fundamentals2. Numerical analysisin a nutshell2.1 Computer arithmeticRepresentation of real numbersMachine precisioExample of limitations of floating point arithmetic2.2 Measuringerrors2.3 Appromating derivatives with finite differencesAppromating first-order derivativesAppromating second-order derivativesPartial derivativesHow to choose hTruncation error for forward difference2.4 Numerical instability and ill-conditioningExample of a numerically unstable algorithmExample of an ill-conditioned problem2.5Condition number of a matrixComments and examples2.6 A primer on algorithmic and computational complety2.6.1 Criteria for comparisoOrder of complety and classificatio2.A Operation count for basiclinear algebra operations3. Linear equations and Least Squares problemsChoice of method3.1 Direct methods3.1.1 Triangular systems3.1.2 LU factorizatio3.1.3 Cholesky factorizatio3.1.4 QRdecompositio3.1.5 Singular value decompositio3.2 Iterative methods3.2.1 Jacobi, Gauss-Seidel, and SORSuccessive overrelaxatio3.2.2 Convergence of niterative methods3.2.3 General structure of algorithms for iterative methods3.2.4 Block iterative methods3.3 Sparse linear systems3.3.1 Tridiagonal systems3.3.2 Irregular sparse matrices3.3.3 Structural properties of sparse matrices3.4 The Least Squares problem3.4.1 Method of normal equations3.4.2 Least Squares via QR factorizatio3.4.3 Least Squares via SVD decompositio3.4.4 Final remarksThe backslash operator in Matlab4. Finite difference methods4.1 An example of a numerical solutioA first numerical appromatioA second numerical appromatio4.2 Classification of differential equations4.3 The Black-Scholes equatio4.3.1 Explicit, implicit, and θ-methods4.3.2 Initial and boundary conditions and definition of thegrid4.3.3 Implementation of the θ-method with Matlab4.3.4 Stability4.3.5 Coordinate transformation of space variables4.4 American options4.A A note on Matlab's function spdiags5.Binomialtrees5.1 MotivatioMatching moments5.2 Growing the tree5.2.1 Implementing a tree5.2.2 Vectorizatio5.2.3 Binomial expansio5.3 Early exerase5.4 Dividends5.5 The GreeksGreeks from the treePart Two Simulation6. Generatmg random numbers6.1 Monte Carlo methods and sampling6.1.1 How it allbega6.1.2 Financialapplications6.2 Uniform random number generators6.2.1 Congruential generators6.2.2 Mersenne Twister6.3 Nonuniform distributions6.3.1 The inversion method6.3.2 Acceptance-rejection method6.4 Specialized methods for selected distributions6.4.1 Normal distributio6.4.2 Higher order moments and the Cornish-Fisher expansio6.4.3 Further distributions6.5 Sampling from a discrete set6.5.1 Discrete uniform selectio6.5.2 Roulette wheel selectio6.5.3 Random permutations and shuffling6.6 Sampling errors-and how to reduce them6.6.1 The basic problem6.6.2 Quasi-Monte Carlo6.6.3 Stratified sampling6.6.4 Variance reductio6.7Drawing from empirical distributions6.7.1 Data randomizatio6.7.2 Bootstrap6.8 Controlled experiments and experimental desig6.8.1 Replicability and ceteris paribus analysis6.8.2 Available random number generators in Matlab6.8.3 Uniform random numbers from Matlab's rand functio6.8.4 Gaussian random numbers from Matlab's randn functio6.8.5 Remedies7.Modelingdependenaes7.1 Transformation methods7.1.1 Linear correlatio7.1.2 Rank correlatio7.2 Markov chains7.2.1 Concepts7.2.2 The Metropolis algorithm7.3 Copula models7.3.1 Concepts7.3.2 Simulation using copulas8. A gentle introduction to financial simulatio8.1 Setting the stage8.2 Single-period simulations8.2.1 Terminal asset prices8.2.2 l-over-N portfolios8.2.3 European options8.2.4 VaR of a covered put portfolio8.3 Simple price processes8.4 Processes with memoryin thelevels of returns8.4.1 Efficient versus adaptive markets8.4.2 Moving averages8.4.3 Autoregressive models8.4.4 Autoregressive moving average （ARMA） models8.4.5 Simulating ARMA models8.4.6 Models withlong-term memory8.5 Time-varying volatility8.5.1 Theconcepts8.5.2 Autocorrelated time-varying volatility8.5.3 Simulating GARCH processes8.5.4 Selected further autoregressive volatility models8.6 Adaptive expectations and patternsin price processes8.6.1 Price-earningsmodels8.6.2 Models with learning8.7Historical simulatio8.7.1 Backtesting8.7.2 Bootstrap8.8 Agent-based models and complety9. Financial simulation at work: some case studies9.1Constant proportion portfolio insurance （CPPI）9.1.1 Basicconcepts9.1.2 Bootstrap9.2 VaR estimation with Extreme Value Theory9.2.1 Basicconcepts9.2.2 Scaling the data9.2.3 Using Extreme Value Theory9.3 Option pricing9.3.1 Modeling prices9.3.2 Pricingmodels9.3.3 Greeks9.3.4 Quasi-Monte CarloPart Three Optimization
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