作者：徐凌//徐梅
页数：170
出版社：南开大学出版社
出版日期：2020
ISBN：9787310059591
电子书格式：pdf/epub/txt
内容简介
本书涉及金融工程方面的信用风险建模研究，主要探讨不接近市场信息下信用风险模型的构建，对于普及信用风险及信用衍生品知识、促进金融创新、加强金融风险管理、推动我国金融竞争力提供了重要的理论依据，有重大的参考作用和借鉴意义。
作者简介
徐凌，中国石油大学(华东)经济管理学院副教授、硕士生导师；研究方向：金融工程、信用风险建模、统计等。出版《人才统计学》等著作2部，发表高水平学术论文10余篇，主持国家自然科学基金、教育部人文社科基金、教育部归国留学基金各1项，参与国家级、省部级、校级教改项目等10余项。
徐梅，中国石油大学(华东)经济管理学院副教授、硕士生导师。
目录
1．1 Preliminary work
1．2 Overview of the book
Chapter 2 Filtering model and the Zakai equation
2．1 Stochastic filtering
2．1．1 A general introduction
2．1．2 The filtering equations
2．1．3 Finite dimensional filters
2．1．4 Filtering from point process observations
2．2 The filtering model
2．2．1 Unobserved state process
2．2．2 Observations
2．2．3 The objective
2．3 The innovations processes
2．4 The Zakai equations
2．4．1 A new measure
2．4．2 The unnormalized filtering equations
Chapter 3 Numerical methods
3．1 A finite dimensional filter
3．1．1 Two special cases
3．1．2 A finite dimensional filter
3．2 The finite-state Markov chain approximation
3．2．1 Approximating Markov chain
3．2．2 Filter
3．2．3 Numerical solution
3．3 Particle methods
Chapter 4 Linear stochastic PDEs
4．1 Semigroup approach
4．1．1 Semigroup
4．1．2 Linear SPDEs
4．2 The variational approach to linear parabolic SPDEs
4．2．1 General setting
4．2．2 Basic results for linear parabolic SPDEs with Gaussiau noise
Chapter 5 Unnormalized conditional density
5．1 Assumptions
5．2 Main results
5．3 Finding the unnormalized conditional density
5．4 Proof of Theorem 5．3
5．4．1 Some existence and uniqueness results on stochastic PDEs
5．4．2 The backward SPDEs
5．4．3 The unnormalized conditional density
Chapter 6 Convergence results
6．1 Introduction
6．2 The mild form of the Zakal equation
6．3 The stochastic integral
6．4 Continuity theorem
6．4．1 Continuity theorem
6．4．2 Proofs
6．5 Galerkin approximation
Chapter 7 Galerkin approximation
7．1 SDEs
7．1．1 Analytical solution
7．1．2 Numerical methods for SDEs
7．2 Basis functions
7．2．1 Gaussiau series
7．2．2 Hermite expansion
7．3 The adaptive Galerkin approximation
7．3．1 Introduction
7．3．2 The adaptive Galerkin approximation
7．3．3 The adaptive Galerkin approximation with Hermite polynomials
7．4 Proofs
7．5 Simulation studies
7．5．1 Tables
7．5．2 Figures
7．5．3 Summary
Appendix A Auxiliary calculations
A．1 Preliminaries
A．1．1 Sobolev spaces
A．1．2 Some spaces of processes
A．2 Some Hilbert spaces
Appendix B List of frequently used notations and symbols
Bibliography
