- 金融数学中的带跳随机微分方程数值解
- - 作者：(澳)普兰顿//(澳)利伯蒂-布鲁迪
  - 出版社：世界图书出版公司
  - ISBN：9787510071188
  - 出版日期：2017/01/01
  - 页数：888
- 售价：50

内容大纲
普兰顿、利伯蒂-布鲁迪著的《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。读者对象：应用数学专业研究生。
作者介绍
目录
Preface
Suggestions for the Reader
Basic Notation
Motivation and Brief Survey
1  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.xercises
2  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  Exercises
3  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  Exercises
4  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  Exercises
6  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  Exercises
7  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  Exercises
8  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 Exercises
9  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  Exercises
10 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 Exercises
11  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 Exercises
12  Regular Weak Taylor Approximations
  12.1 Weak Taylor Schemes
  12.2 Commutativity Conditions
  12.3 Convergence Results
  12.4 Exercises
13  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 Exercises
14 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 Exercises
15  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 Exercises
16  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 Exercises
17  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 Exercises
18  Solutions for Exercises
Acknowledgements
Bibliographical Notes
References
Author Index
Index

内容大纲

作者介绍

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