金融数学中的带跳随机微分方程数值解
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作者Eckhard Platen，Nicola Bruti-Liberati[著]
出版社世界图书出版公司北京公司
ISBN9787510071188
出版时间2017-01
装帧平装
开本其他
定价125元
货号8948244
上书时间2024-09-07
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作者简介
Eckhard Platen , Nicola Bruti-Liberati是澳大利亚的金融统计领域的学者
目录
PrefaceSuggestions for the ReaderBasic NotationMotivation and Brief Survey1 Stochastic Differential Equations with Jumps.
1.1 Stochastic Processes 1.2 Supermartingales and Martingales 1.3 Quadratic Variation and Covariation 1.4 Ito Integral 1.5 It5 Formula 1.6 Stochastic Differential Equations 1.7 Linear SDEs 1.8 SDEs with Jumps 1.9 Existence and Uniqueness of Solutions of SDEs.
1.10 E.xercises2 Exact Simulation of Solutions of SDEs 2.1 Motivation of Exact Simulation 2.2 Sampling from Transition Distributions 2.3 Exact Solutions of Multi-dimensional SDEs 2.4 Functions of Exact Solutions 2.5 Almost Exact Solutions by Conditioning 2.6 Almost Exact Simulation by Time Change 2.7 Functionals of Solutions of SDEs 2.8 Exercises3 Benchmark Approach to Finance and Insurance 3.1 Market Model 3.2 Best Performing Portfolio 3.3 Supermartingale Property and Pricing 3.4 Diversification 3.5 Real World Pricing Under Some Models 3.6 Real World Pricing Under the MMM 3.7 Binomial Option Pricing 3.8 Exercises4 Stochastic Expansions 4.1 Introduction to Wagner-Platen Expansions 4.2 Multiple Stochastic Integrals 4.3 Coefficient Functions 4.4 Wagner-Platen Expansions 4.5 Moments of Multiple Stochastic Integrals 4.6 Exercises Introduction to Scenario Simulation 5.1 Approximating Solutions of ODEs 5.2 Scenario Simulation 5.3 Strong Taylor Schemes 5.4 Derivative-Free Strong Schemes 5.5 Exercises6 Regular Strong Taylor Approximations with Jumps 6.1 Discrete-Time Approximation 6.2 Strong Order 1.0 Taylor Scheme 6.3 Commutativity Conditions 6.4 Convergence Results 6.5 Lemma on Multiple It5 Integrals 6.6 Proof of the Convergence Theorem 6.7 Exercises7 Regular Strong It6 Approximations 7.1 Explicit Regular Strong Schemes 7.2 Drift-Implicit Schemes 7.3 Balanced Implicit Methods 7.4 Predictor-Corrector Schemes 7.5 Convergence Results 7.6 Exercises8 Jump-Adapted Strong Approximations 8.1 Introduction to Jump-Adapted Approximations 8.2 Jump-Adapted Strong Taylor Schemes 8.3 Jump-Adapted Derivative-Free Strong Schemes.
8.4 Jump-Adapted Drift-Implicit Schemes 8.5 Predictor-Corrector Strong Schemes 8.6 Jump-Adapted Exact Simulation 8.7 Convergence Results 8.8 Numerical Results on Strong Schemes 8.9 Approximation of Pure Jump Processes 8.10 Exercises9 Estimating Discretely Observed Diffusions 9.1 Maximum Likelihood Estimation 9.2 Discretization of Estimators 9.3 Transform Functions for Diffusions 9.4 Estimation of Affine Diffusions 9.5 Asymptotics of Estimating Functions 9.6 Estimating Jump Diffusions 9.7 Exercises10 Filtering 10.1 Kalman-Bucy Filter 10.2 Hidden Markov Chain Filters 10.3 Filtering a Mean Reverting Process 10.4 Balanced Method in Filtering 10.5 A Benchmark Approach to Filtering in Finance 10.6 Exercises11 Monte Carlo Simulation of SDEs 11.1 Introduction to Monte Carlo Simulation 11.2 Weak Taylor Schemes 11.3 Derivative-Free Weak Approximations 11.4 Extrapolation Methods 11.5 Implicit and Predictor-Corrector Methods 11.6 Exercises12 Regular Weak Taylor Approximations 12.1 Weak Taylor Schemes 12.2 Commutativity Conditions 12.3 Convergence Results 12.4 Exercises13 Jump-Adapted Weak Approximations 13.1 Jump-Adapted Weak Schemes 13.2 Derivative-Free Schemes 13.3 Predictor-Corrector Schemes 13.4 Some Jump-Adapted Exact Weak Schemes 13.5 Convergence of Jump-Adapted Weak Taylor Schemes 13.6 Convergence of Jump-Adapted Weak Schemes 13.7 Numerical Results on Weak Schemes 13.8 Exercises14 Numerical Stability 14.1 Asymptotic p-Stability 14.2 Stability of Predictor-Corrector Methods 14.3 Stability of Some Implicit Methods 14.4 Stability of Simplified Schemes 14.5 Exercises15 Martingale Representations and Hedge Ratios 15.1 General Contingent Claim Pricing 15.2 Hedge Ratios for One-dimensional Processes 15.3 Explicit Hedge Ratios 15.4 Martingale Representation for Non-Smooth Payoffs ..
15.5 Absolutely Continuous Payoff ~nctions 15.6 Maximum of Several Assets 15.7 Hedge Ratios for Lookback Options 15.8 Exercises16 Variance Reduction Techniques 16.1 Various Variance Reduction Methods 16.2 Measure Transformation Techniques 16.3 Discrete-Time Variance Reduced Estimators 16.4 Control Variates 16.5 HP Variance Reduction 16.6 Exercises17 Trees and Markov Chain Approximations 17.1 Numerical Effects of Tree Methods 17.2 Efficiency of Simplified Schemes 17.3 Higher Order Markov Chain Approximations 17.4 Finite Difference Methods 17.5 Convergence Theorem for Markov Chains 17.6 Exercises18 Solutions for ExercisesAcknowledgementsBibliographical NotesReferencesAuthor IndexIndex
内容摘要
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精彩内容
《金融数学中的带跳随机微分方程数值解》主要阐述Wiener和Possion过程或者Possion跳度形成的随机微分方程的离散时间分散值的设计和分析。在金融和精算模型中及其他应用领域，这样的跳跃扩散常被用来描述不同状态变量的动态。在金融领域，这些可能代表资产价格，信用等级，股票指数，利率，外汇汇率或商品价格。本书主要介绍离散随机方程的近似离散值解的有效性和数值稳定性。
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