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A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems such as portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed.
List of contents
Weack Convergence of Stochastic Processes: Basic Properties of Stochastic Processes.- Weak Convergence.- Weak Convergence to a Semimartingale.- Weak Convergence of Stochastic Integrals.- Limit Theorems, Density Processes and Contiguity.- Weak Convergence of Financial Markets: Convergence of Optimal Consumption-Portfolio Strategies.- Convergence of Option Prices.- Convergence of Hedging Strategies.- The Basic Models of Approximations: General Remarks.- Lattice.- Alternative Approximations.- Approximations of Term Structure Models.- Index.
Summary
A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems such as portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed.
Additional text
From the reviews:
"A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. … The third part deals with lattice- and tree-based computational procedures for option pricing … . Includes detailed examples." (www.mathfinance.de, November, 2003)
"The book recalls techniques and results of weak convergence of stochastic processes in mathematical finance and covers a wide range of applications. … For readers very well acquainted with the material, it may serve as a good reference book on the subject." (F. Esche, Short Book Reviews, Vol. 24 (1), 2004)
Report
From the reviews:
"A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. ... The third part deals with lattice- and tree-based computational procedures for option pricing ... . Includes detailed examples." (www.mathfinance.de, November, 2003)
"The book recalls techniques and results of weak convergence of stochastic processes in mathematical finance and covers a wide range of applications. ... For readers very well acquainted with the material, it may serve as a good reference book on the subject." (F. Esche, Short Book Reviews, Vol. 24 (1), 2004)
