Kianoush Fathi vajargah - Department of Statistics, Islamic Azad University, North branch, Tehran, Iran,
Hamid Mottaghi Golshan - Department of Mathematics, Shahriar Branch, Islamic Azad University, Shahriar, Iran
Abbas Arjomandfar - Department of Mathematics, Yadegar-e-Imam Khomeini (RAH), Shahrerey Branch, Islamic Azad University, Tehran, Iran

In this paper, first, the stochastic differential equations are introduced as well as the definition and basic theories about Monte Carlo and quasi-Monte Carlo and Sobel and Halton sequences are expressed. Indeed, we introduce and use simulations under these methods to compare the efficiency of the solutions, which the results show that the approximation of the resulting Sobel sequence is much better than other stochastic methods. The comparison of the efficiency of random and quasi-random methods, the geometric Brownian movement and the price index of Tehran stock (equal weight and weight-value) is studied. The results show that the quasi-Monte Carlo method is better than other methods.

Stochastic Differential Equation, random sequence, Quasi-random sequence, (Quasi) Monte Carlo simulation