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Stochastic Analysis and Applications to Finance
A collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. It covers the topics ranging from Markov processes, backward stochastic differential equations, stochastic partial differential equations, and stochastic control, to risk measure and risk theory.
Hilbert-huang Transform And Its Applications (2nd Edition)
This book is written for scientists and engineers who use HHT (Hilbert-Huang Transform) to analyze data from nonlinear and non-stationary processes. It can be treated as a HHT user manual and a source of reference for HHT applications. The book contains the basic principle and method of HHT and various application examples, ranging from the correction of satellite orbit drifting to detection of failure of highway bridges.The thirteen chapters of the first edition are based on the presentations made at a mini-symposium at the Society for Industrial and Applied Mathematics in 2003. Some outstanding mathematical research problems regarding HHT development are discussed in the first three chapters. The three new chapters of the second edition reflect the latest HHT development, including ensemble empirical mode decomposition (EEMD) and modified EMD.The book also provides a platform for researchers to develop the HHT method further and to identify more applications.
Control Theory and Related Topics
Xunjing Li (1935OCo2003) was a pioneer in control theory in China. He was known in the Chinese community of applied mathematics, and in the global community of optimal control theory of distributed parameter systems. He has made important contributions to the optimal control theory of distributed parameter systems, in particular regarding the first-order necessary conditions (Pontryagin-type maximum principle) for optimal control of nonlinear infinite-dimensional systems. He directed the Seminar of Control Theory at Fudan towards stochastic control theory in 1980s, and mathematical finance in 1990s, which has led to several important subsequent developments in both closely interactive fields...
Hilbert-Huang Transform and Its Applications
This book is written for scientists and engineers who use HHT (HilbertOCoHuang Transform) to analyze data from nonlinear and non-stationary processes. It can be treated as a HHT user manual and a source of reference for HHT applications. The book contains the basic principle and method of HHT and various application examples, ranging from the correction of satellite orbit drifting to detection of failure of highway bridges. The thirteen chapters of the first edition are based on the presentations made at a mini-symposium at the Society for Industrial and Applied Mathematics in 2003. Some outstanding mathematical research problems regarding HHT development are discussed in the first three cha...
Control Theory And Related Topics: In Memory Of Professor Xunjing Li
Xunjing Li (1935-2003) was a pioneer in control theory in China. He was known in the Chinese community of applied mathematics, and in the global community of optimal control theory of distributed parameter systems. He has made important contributions to the optimal control theory of distributed parameter systems, in particular regarding the first-order necessary conditions (Pontryagin-type maximum principle) for optimal control of nonlinear infinite-dimensional systems. He directed the Seminar of Control Theory at Fudan towards stochastic control theory in 1980s, and mathematical finance in 1990s, which has led to several important subsequent developments in both closely interactive fields. These remarkable efforts in scientific research and education, among others, gave birth to the so-called “Fudan School”.This proceedings volume includes a collection of original research papers or reviews authored or co-authored by Xunjing Li's former students, postdoctoral fellows, and mentored scholars in the areas of control theory, dynamic systems, mathematical finance, and stochastic analysis, among others.
Hierarchical Decision Making in Stochastic Manufacturing Systems
One of the most important methods in dealing with the optimization of large, complex systems is that of hierarchical decomposition. The idea is to reduce the overall complex problem into manageable approximate problems or subproblems, to solve these problems, and to construct a solution of the original problem from the solutions of these simpler prob lems. Development of such approaches for large complex systems has been identified as a particularly fruitful area by the Committee on the Next Decade in Operations Research (1988) [42] as well as by the Panel on Future Directions in Control Theory (1988) [65]. Most manufacturing firms are complex systems characterized by sev eral decision subsystems, such as finance, personnel, marketing, and op erations. They may have several plants and warehouses and a wide variety of machines and equipment devoted to producing a large number of different products. Moreover, they are subject to deterministic as well as stochastic discrete events, such as purchasing new equipment, hiring and layoff of personnel, and machine setups, failures, and repairs.
Discrete-Time Markov Chains
This book focuses on two-time-scale Markov chains in discrete time. Our motivation stems from existing and emerging applications in optimization and control of complex systems in manufacturing, wireless communication, and ?nancial engineering. Much of our e?ort in this book is devoted to designing system models arising from various applications, analyzing them via analytic and probabilistic techniques, and developing feasible compu- tionalschemes. Ourmainconcernistoreducetheinherentsystemcompl- ity. Although each of the applications has its own distinct characteristics, all of them are closely related through the modeling of uncertainty due to jump or switching random processes. Oneofthesali...
Probability, Finance And Insurance, Proceedings Of A Workshop
This workshop was the first of its kind in bringing together researchers in probability theory, stochastic processes, insurance and finance from mainland China, Taiwan, Hong Kong, Singapore, Australia and the United States. In particular, as China has joined the WTO, there is a growing demand for expertise in actuarial sciences and quantitative finance. The strong probability research and graduate education programs in many of China's universities can be enriched by their outreach in fields that are of growing importance to the country's expanding economy, and the workshop and its proceedings can be regarded as the first step in this direction.This book presents the most recent developments ...
Kernel-based Approximation Methods Using Matlab
In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.
Contract Theory in Continuous-Time Models
In recent years there has been a significant increase of interest in continuous-time Principal-Agent models, or contract theory, and their applications. Continuous-time models provide a powerful and elegant framework for solving stochastic optimization problems of finding the optimal contracts between two parties, under various assumptions on the information they have access to, and the effect they have on the underlying "profit/loss" values. This monograph surveys recent results of the theory in a systematic way, using the approach of the so-called Stochastic Maximum Principle, in models driven by Brownian Motion. Optimal contracts are characterized via a system of Forward-Backward Stochastic Differential Equations. In a number of interesting special cases these can be solved explicitly, enabling derivation of many qualitative economic conclusions.
