Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option

Nonlinearities distribution Laplace transform-homotopy perturbation method

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we ...

Analytical Solution of Fractional Black-scholes European Option Pricing Equation by Using Laplace Transform

In this paper, Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method, is employed to obtain a quick and accurate solution to the fractional Black Scholes equation with boundary condition for a European option pricing problem. The Black-Scholes formula is used as a model for valuing European or American call and put options on ...

European option pricing of fractional Black-Scholes model with new Lagrange multipliers

In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to  btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

Solving The Optimal Control Problems Using Homotopy Perturbation Transform Method

Inthispaper,wesolveHamilton-Jocobi-Bellman(HJB)equationsarisinginoptimalcontrolproblems usingHomotopyPerturbationTransformMethod(HPTM).Theproposedmethodisacombinedform oftheLaplaceTransformationMethodwiththeHomotopyPerturbationMethodtoproduceahighly effectivemethodtohandlemanyproblems. ApplyingtheHPTM,solutionprocedurebecomeseasier, simplerandmorestraightforward. Someillustrativeexamplesaregive...