Name: Generalized Integral Transforms in Mathematical Finance
Brand: Atlantic Books
SKU: 9789811231735
Price: 16196.0 INR
Availability: InStock

Generalized Integral Transforms in Mathematical Finance

by Andrey Itkin , Alexander Lipton , Dmitry Muravey

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ISBN13: 9789811231735
Binding: Hardcover
Subject: N/A
Publisher: World Scientific Publishing Company
Publisher Imprint: World Scientific Publishing Company
Publication Date: October 28, 2021
Pages: 508
Original Price: USD 168.0
Language: English
Edition: N/A
Item Weight: 844 grams
BISAC Subject(s): Finance / Financial Engineering

About The Book

This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model with default contagion; (c) finding first hitting time density for a reducible diffusion process; (d) describing the exercise boundary of American options; (e) calculating default boundary for the structured default problem; (f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.The main methods used in this book are generalized integral transforms and heat potentials. To find a semi-closed form solution, we need to solve a linear or nonlinear Volterra equation of the second kind and then represent the option price as a one-dimensional integral. Our analysis shows that these methods are computationally more efficient than the corresponding finite-difference methods for the backward or forward Kolmogorov PDEs (partial differential equations) while providing better accuracy and stability.We extend a large number of known results by either providing solutions on complementary or extended domains where the solution is not known yet or modifying these techniques and applying them to new types of equations, such as the Bessel process. The book contains several novel results broadly applicable in physics, mathematics, and engineering.

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