TY - BOOK

T1 - Numerical Methods for Nonlinear PDEs in Finance

AU - Mashayekhi, Sima

PY - 2015

Y1 - 2015

N2 - Nonlinear Black-Scholes equations arise from considering parameters such as feedbackand illiquid markets eects or large investor preferences, volatile portfolio and nontrivialtransaction costs into option pricing models to have more accurate option price. Heresome nite dierence schemes have been investigated to solve numerically such nonlinearequations.However the analytical solution of the linear Black-Scholes equation is known, dierentnumerical methods have been considered for solving the equation to make a general numericalscheme for solving other more complicated models with no analytical solutionssuch as nonlinear Black-Scholes models. Therefore at rst some investigations for thestandard linear Black-Scholes equation have been considered for instance choosing a suitableright boundary condition and applying some remedies for dealing with nonsmoothconditions of the equation. After that a number of nonlinear Black-Scholes models arereviewed and dierent numerical methods have been investigated for solving some ofthose models. At the end the numerical schemes have been compared with respect toorder of convergence.

AB - Nonlinear Black-Scholes equations arise from considering parameters such as feedbackand illiquid markets eects or large investor preferences, volatile portfolio and nontrivialtransaction costs into option pricing models to have more accurate option price. Heresome nite dierence schemes have been investigated to solve numerically such nonlinearequations.However the analytical solution of the linear Black-Scholes equation is known, dierentnumerical methods have been considered for solving the equation to make a general numericalscheme for solving other more complicated models with no analytical solutionssuch as nonlinear Black-Scholes models. Therefore at rst some investigations for thestandard linear Black-Scholes equation have been considered for instance choosing a suitableright boundary condition and applying some remedies for dealing with nonsmoothconditions of the equation. After that a number of nonlinear Black-Scholes models arereviewed and dierent numerical methods have been investigated for solving some ofthose models. At the end the numerical schemes have been compared with respect toorder of convergence.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122158646305763

M3 - Ph.D. thesis

SN - 978-87-7078-935-6:

BT - Numerical Methods for Nonlinear PDEs in Finance

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -