Generalized Integral Transforms In Mathematical Finance

This book uses techniques from physics to solve mathematical finance problems with moving boundaries, such as pricing options, analyzing banking systems, and optimal trading strategies. It provides more efficient and accurate solutions than finite-difference methods and extends known results to new types of equations.

Format: Hardback
Length: 508 pages
Publication date: 28 October 2021
Publisher: World Scientific Publishing Co Pte Ltd

This comprehensive book delves into a range of techniques initially developed in physics for solving problems related to heat and mass transfer, and it applies these methodologies to diverse mathematical finance problems defined in domains with moving boundaries. These problems encompass a wide spectrum, including:

Semi-Closed Form Pricing of Options in One-Factor Models with Time-Dependent Barriers: This involves pricing options in models such as Bachelier, Hull-White, CIR, and CEV, where the barriers are time-dependent. The book employs generalized integral transforms and heat potentials to derive semi-closed form solutions for these pricing problems.

Analyzing an Interconnected Banking System in the Structural Credit Risk Model with Default Contagion: The book explores the analysis of an interconnected banking system using the structural credit risk model, which considers default contagion among banks. It employs techniques such as generalized integral transforms and heat potentials to assess the risk and stability of the banking system.

Finding First Hitting Time Density for a Reducible Diffusion Process: This involves determining the time density at which a stochastic process reaches a certain threshold or hits a boundary. The book employs generalized integral transforms and heat potentials to solve this problem and obtain accurate results.

Describing the Exercise Boundary of American Options: This involves understanding the behavior of American options, which are financial instruments with limited exercise periods. The book employs generalized integral transforms and heat potentials to describe the exercise boundary and calculate the value of American options.

Calculating Default Boundary for the Structured Default Problem: This involves solving a boundary value problem related to the default of a structured financial instrument. The book employs generalized integral transforms and heat potentials to derive a semi-closed form solution for this problem.

Deriving a Semi-Closed Form Solution for Optimal Mean-Reverting Trading Strategies: This involves developing a semi-closed form solution for optimal mean-reverting trading strategies, which are used in financial markets to exploit market inefficiencies. The book employs generalized integral transforms and heat potentials to derive these trading strategies.

To achieve these solutions, the book utilizes a combination of main methods, including generalized integral transforms and heat potentials. These methods offer computational efficiency compared to finite-difference methods for backward or forward Kolmogorov PDEs (partial differential equations). Furthermore, they provide improved accuracy and stability in solving these complex problems.

By extending a wide range of known results and modifying these techniques, the book explores new applications in physics, mathematics, and engineering. It presents novel results that have broad implications across these fields.

Overall, this book is a valuable resource for researchers, practitioners, and students interested in applied mathematics, financial engineering, and computational science. It provides a comprehensive treatment of the techniques and applications related to heat and mass transfer, making it an essential tool for understanding and solving complex problems in these domains.

ISBN-13: 9789811231735