Quasilinearization numerical scheme for fully nonlinear parabolic problems with applications in models of mathematical finance
نویسندگان
چکیده
منابع مشابه
A numerical scheme for solving nonlinear backward parabolic problems
In this paper a nonlinear backward parabolic problem in one dimensional space is considered. Using a suitable iterative algorithm, the problem is converted to a linear backward parabolic problem. For the corresponding problem, the backward finite differences method with suitable grid size is applied. It is shown that if the coefficients satisfy some special conditions, th...
متن کاملa numerical scheme for solving nonlinear backward parabolic problems
in this paper a nonlinear backward parabolic problem in one dimensional space is considered. using a suitable iterative algorithm, the problem is converted to a linear backward parabolic problem. for the corresponding problem, the backward finite differences method with suitable grid size is applied. it is shown that if the coefficients satisfy some special conditions, th...
متن کاملQuasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence
We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function. 2000 Mathematics Subject Classification: 35K10, 35K15, 35R10.
متن کاملA Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs
We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in [10], and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretizat...
متن کاملMathematical finance: basic models and unsolved problems
Mathematical finance is a relatively new mathematical field. It was in a phase of explosive growth last 10-15 years, and there is very indication it will continue growing for a while yet. The growth is due to a combination of demand from financial institutions and a breakthrough in the mathematical theory of option pricing. The talk will outline basic mathematical theorems and ideas used here, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2013
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2013.01.008