000 02589nam a22003135i 4500
003 CUTN
005 20250527171324.0
008 210721s2021 nju 000 0 eng
020 _a9789811231735
020 _z9789811231742
020 _z9789811231759
041 _aEnglish
042 _apcc
082 _a332.015
_bITK
100 1 _aItkin, Andrey,
100 1 _eauthor.
245 1 0 _aGeneralized Integral Transforms in Mathematical Finance /
_cAndrey Itkin, Alexander Lipton, Dmitry Muravey.
260 _aSingapore :
_bWorld Scientific Publishing Company,
_c2022.
263 _a2108
300 _axxxiii, 473 pages :
_billustrations (black and white, some color) ;
_c24 cm.
520 _a"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"--
700 1 _aLipton, Alexander,
700 1 _aMuravey, Dmitry,
700 1 _eauthor.
700 1 _eauthor.
906 _a0
_bibc
_corignew
_d2
_eepcn
_f20
_gy-gencatlg
942 _2ddc
_cBOOKS
999 _c44389
_d44389