In this paper, we consider a method for solving a linear programming problem with fuzzy objective and coefficient matrix, where the fuzzy numbers are supposed to be triangular. By the proposed method, the Decision Maker will have the flexibility of choosing. The solving method is based on the Pareto algorithm, which converts the problem to a weighted-objective linear programming. For more illustration, after discussing the problem and the algorithm, we present an example, which its solutions are independent from the objective weights.

The purpose of this paper is to survey stochastic differential equations and Euler-Maruyama method for approximating the solution to these equations in financial problems. It is not possible to get explicit solution and analytically answer for many of stochastic differential equations, but in the case of linear stochastic differential equations it may be possible to get an explicit answer. We can approximate the solution with standard numerical methods, such as Euler-Maruyama method, Milstein method and Runge-Kutta method. We will use Euler-Maruyama method for simulation of stochastic differential equations for financial problems, such as asset pricing model, square-root asset pricing model, payoff for a European call option and estimating value of European call option and Asian option to buy the asset at the future time. We will discuss how to find the approximated solutions to stochastic differential equations for financial problems with examples.

In this paper, first derivative of smooth function is defined by the optimal solution of a special optimization problem. In the next step, by using this optimization problem for nonsmooth function, we obtain an approximation for first derivative of nonsmooth function which it is called generalized first derivative. We then extend it to define generalized second derivative for nonsmooth function. Finally, we show the efficiency of our approach by evaluating derivative and generalized first and second derivative of some smooth and nonsmooth functions, respectively.