An exact and explicit solution for the valuation of American put options
By Song‐Ping Zhu. 2006
269 citations recorded by the source corpus.
Subfields: Finance
View Paper: https://www.semanticscholar.org/paper/d8db2f35b07e85be8b3c688fa41a304a574b1ffc
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Citations in the corpus
- On the relationship between the homotopy analysis method and Euler transform (2010, methodology): “Thereafter, the HAM has been improved step by step [14–20] and has been widely applied in science, engineering and finance [21–29].”
- A new analytical technique to solve Volterra's integral equations (2011, background): “Then, by Equations (9)–(11) and with the help of (3) we have um(x) = um−1(x)−Rm(−→u m−1, x) = um−1(x)− 1 (m−1)! m−1N [∑n=+∞ n=0 un(x)pn ] pm−1 ∣∣∣∣∣∣ p=0 = um−1(x)− m−1 [∑n=+∞ n=0 un(x)pn −f (x)− ∫ x a K(x, t) [ L [∑n=+∞ n=0 un(t)pn ] +N [∑n=+∞ n=0 un(t)pn ]] dt ] (m−1)! pm−1 ∣∣∣∣∣∣ p=0 .”
- A new branch of solutions of boundary-layer flows over a permeable stretching plate (2007, methodology): “For example, Zhu [46,47] applied the HAM to obtain, for the first time, an explicit series solution of the famous Black–Scholes type equation in finance for American put option, which is a system of non-linear PDEs with an unknown moving boundary.”
- Homotopy Analysis Method in Nonlinear Differential Equations (2012, methodology): “In fact, the HAM even logically contains the Euler transform: we can derive the famous Euler transform in the frame of the HAM, and give a similar but more general transform, called the generalized Euler transform, as shown in Chapter 5.”
- Notes on the homotopy analysis method: Some definitions and theorems (2009, methodology): “Since Liao’s book [21] for the homotopy analysis method was published in 2003, more and more researchers have been successfully applying this method to various nonlinear problems in science and engineering, such as the viscous flows of non-Newtonian fluids [28–38], the KdV-type equations [39–43], no”
- An optimal homotopy-analysis approach for strongly nonlinear differential equations (2010, methodology): “The HAM has been widely applied to solve different types of nonlinear problems in science, finance and engineering [37,32,23,33,38–43,34,44– 48,35,36,49,50].”
- A general approach to get series solution of non-similarity boundary-layer flows (2009, methodology): “Furthermore, the homotopy analysis method has been applied to solve some non-linear partial differential equations, such as unsteady similarity boundary-layer flows [40], Black–Scholes type equation in finance for American put option [52,53] and interaction of non-linear water wave and exponential s”