Generalized Integral Transforms In Mathematical Finance
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€192.20
A01=Alexander Lipton
A01=Andrey Itkin
A01=Dmitry Muravey
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American Options
Author_Alexander Lipton
Author_Andrey Itkin
Author_Dmitry Muravey
Barrier Options
Category=PBW
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
First Hitting Time Density
Generalized Integral Transforms
Heat Potentials
Mathematical Finance
Moving Boundaries
Partial Differential Equations
Semi-Closed Form Solutions
Time-Dependent Barrier
Product details
- ISBN 9789811231735
- Publication Date: 28 Oct 2021
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
