数理金融基准分析方法 内容简介

《数理金融基准分析法》分两个部分。**部分介绍了概率理论、统计学、随机微积分以及带跳跃的随机微分方程中的一些必要工具。第二部分专门介绍了基准分析法的金融建模。这一部分对衍生工具的真实世界定价与对冲的多种数量方法进行了解释。其应用的一般性框架可以增进读者对随机波动率本质的了解。该书适用于数量分析师、研究生以及金融、经济和保险领域的从业人士。

数理金融基准分析方法 本书特色

《数理金融基准分析法》分两个部分。**部分介绍了概率理论、统计学、随机微积分以及带跳跃的随机微分方程中的一些必要工具。第二部分专门介绍了基准分析法的金融建模。这一部分对衍生工具的真实世界定价与对冲的多种数量方法进行了解释。其应用的一般性框架可以增进读者对随机波动率本质的了解。该书适用于数量分析师、研究生以及金融、经济和保险领域的从业人士。

数理金融基准分析方法 目录

Basic Notation1Preliminaries from Probability Theory1.1Discrete Random Variables and Distributions1.2Continuous Random Variables and Distributions1.3Moments of Random Variables1.4Joint Distributions and Random Vectors1.5Copulas (*)1.6Exercises for Chapter 12Statistical Methods2.1Limit Theorems2.2Confidence Intervals2.3Estimation Methods2.4Maximum Likelihood Estimation2.5Normal Variance Mixture Models2.6Distribution of Index Log-Returns2.7Convergence of Random Sequences2.8Exercises for Chapter 23Modeling via Stochastic Processes3.1Introduction to Stochastic Processes3.2Certain Classes of Stochastic Processes3.3Discrete Time Markov Chains3.4Continuous Time Markov Chains3.5Poisson Processes3.6Levy Processes (*)3.7Insurance Risk Modeling (*)3.8Exercises for Chapter 34 Diffusion Processes4.1Continuous Markov Processes4.2Examples for Continuous Markov Processes4.3Diffusion Processes4.4Kolmogorov Equations4.5Diffusions with Stationary Densities4.6Multi-Dimensional Diffusion Processes (*)4.7Exercises for Chapter 45 Martingales and Stochastic Integrals5.1Martingales5.2Quadratic Variation and Covariation5.3Gains from Trade as Stochastic Integral5.4It5 Integral for Wiener Processes5.5Stochastic Integrals for Semimartingales (*)5.6Exercises for Chapter 56 The It6 Formula6.1The Stochastic Chain Rule6.2Multivariate It5 Formula6.3Some Applications of the It5 Formula6.4Extensions of the It5 Formula6.5Levy's Theorem (*)6.6A Proof of the It5 Formula (*)6.7Exercises for Chapter 67 Stochastic Differential Equations7.1Solution of a Stochastic Differential Equation7.2Linear SDE with Additive Noise7.3Linear SDE with Multiplicative Noise7.4Vector Stochastic Differential Equations7.5Constructing Explicit Solutions of SDEs7.6Jump Diffusions (*)7.7Existence and Uniqueness (*)7.8Markovian Solutions of SDEs (*)7.9Exercises for Chapter 78 Introduction to Option Pricing8.1Options8.2Options under the Black-Scholes Model8.3The Black-Scholes Formula8.4Sensitivities for European Call Option8.5European Put Option8.6Hedge Simulation8.7Squared Bessel Processes (*)8.8Exercises for Chapter 89 Various Approaches to Asset Pricing9.1Real World Pricing9.2Actuarial Pricing9.3Capital Asset Pricing Model9.4Risk Neutral Pricing9.5Girsanov Transformation and Bayes Rule (*)9.6Change of Numeraire (*)9.7Feynman-Kac Formula (*)9.8Exercises for Chapter 910Continuous Financial Markets10.1Primary Security Accounts and Portfolios10.2Growth Optimal Portfolio10.3Supermartingale Property10.4Real World Pricing10.5GOP as Best Performing Portfolio10.6Diversified Portfolios in CFMs10.7Exercises for Chapter 1011Portfolio Optimization11.1Locally Optimal Portfolios11.2Market Portfolio and GOP11.3Expected Utility Maximization11.4Pricing Nonreplicable Payoffs11.5Hedging11.6Exercises for Chapter 1112Modeling Stochastic Volatility12.1Stochastic Volatility12.2Modified CEV Model12.3Local Volatility Models12.4Stochastic Volatility Models12.5Exercises for Chapter 1213Minimal Market Model13.1Parametrization via Volatility or Drift13.2Stylized Minimal Market Model13.3Derivatives under the MMM13.4MMM with Random Scaling (*)13.5Exercises for Chapter 1314Markets with Event Risk14.1Jump Diffusion Markets14.2Diversified Portfolios14.3Mean-Variance Portfolio Optimization14.4Real World Pricing for Two Market Models14.5Exercises for Chapter 1415Numerical Methods15.1Random Number Generation15.2Scenario Simulation15.3Classical Monte Carlo Method15.4Monte Carlo Simulation for SDEs15.5Variance Reduction of Functionals of SDE15.6Tree Methods15.7Finite Difference Methods15.8Exercises for Chapter 1516Solutions for ExercisesAcknowledgementsReferencesAuthor IndexIndex

数理金融基准分析方法 作者简介

Eckhard Platen(E. 普拉滕, 澳大利亚) 是国际知名学者，在数学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。