classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...

Black-Scholes equation as one of the most celebrated mathematical models has an explicit analytical solution known formula. Later variations equation, such fractional or nonlinear equations, do not have a closed form expression for corresponding In that case, will need asymptotic expansions, homotopy perturbation method, to give approximate solution. However, is non-smooth at special point. We ...

Abstract This manuscript is involved in the study of stability solutions functional differential equations (FDEs) with random coefficients and/or stochastic terms. We focus on different types random/stochastic systems, specifically, delay (SDDEs). Introducing appropriate Lyapunov functionals enables us to investigate necessary conditions for stability, asymptotic mean square exponential global ...

The Black-Scholes equations have been increasingly popular over the last three decades since they provide more practical information for optional behaviours. Therefore, effective methods needed to analyze these models. This study will focus mainly on investigating behavior of equation European put option pricing model. To achieve this, numerical solutions model are produced by combined methods....

In this paper, installment options on the underlying asset which evolves according to Black-Scholes model and pays constant dividend to its owner will be considered. Applying arbitrage pricing theory, the non-homogeneous parabolic partial differential equation governing the value of installment option is derived. Then, penalty method is used to value the European continuous installment call opt...