عبدالمجید عبدالباقی عطاءآبادی

In this paper, we use fuzzy numbers and possibility theory to model possibility. The purpose of this work is to determine the optimal investment model based on the neural network method for fuzzy LR, trapezoidal and triangular numbers in an optimal portfolio. It is listed on the Tehran Stock Exchange to maximize "returns" and reduce "risk" to find the optimal portfolio. Therefore, to achieve this goal, the problem of multi-objective nonlinear programming is addressed. Also, by substituting the mean-variance model and the standard mean deviation instead of the Markowitz mean-variance model, the selection of the optimal portfolio in the possible space is examined. Finally, after calculating the model of the possibility of fuzzy numbers, we reach the optimal stock portfolio, which can be used to set the stock portfolio that has the highest returns and the lowest risk.

In this article, the pricing of option contracts is discussed using the Mikhailov and Nogel model and the artificial neural network method. The purpose of this research is to investigate and compare the performance of various types of activator functions available in artificial neural networks for the pricing of option contracts. The Mikhailov and Nogel model is the same model that is dependent on time. In the design of the artificial neural network required for this research, the parameters of the Mikhailov and Nogel model have been used as network inputs, as well as 700 data from the daily price of stock options available in the Tehran Stock Exchange market (in 2021) as the net-work output. The first 600 data are considered for learning and the remaining data for comparison and conclusion. At first, the pricing is done with 4 commonly used activator functions, and then the results of each are com-pared with the real prices of the Tehran Stock Exchange to determine which item provides a more accurate forecast. The results obtained from this re-search show that among the activator functions available in this research, the ReLU activator function performs better than other activator functions.

In this paper, the European option pricing is done using neural networks in the Black-Scholes-Vasicek market. The general purpose of this research is to compare the accuracy of neural network and Black-Scholes-Vasicek models for the pricing of call options. In the sequel, the finite difference method is applied to find approximate solutions of partial differential equation related to option pricing in the considered market. In the design of the artificial neural network required for this research, the parameters of the Black-Scholes-Vasicek model have been used as network inputs, as well as 720 data from the daily price of stock options available in the Tehran Stock Exchange market (in 1400) as the network output. The approximate solutions obtained in this article, which were carried out by two methods of neural networks and finite differences on the Tehran stock exchange based on the daily price of stock options, are shown that neural networks are more accurate method comparing with finite difference. The comparison of pricing results using neural networks with real prices in the assumed market is presented and shown via diagram, as well. In this paper, the European option pricing is done using neural networks in the Black-Scholes-Vasicek market. The general purpose of this research is to compare the accuracy of neural network and Black-Scholes-Vasicek models for the pricing of call options. In the sequel, the finite difference method is applied to find approximate solutions of partial differential equation related to option pricing in the considered market. In the design of the artificial neural network required for this research, the parameters of the Black-Scholes-Vasicek model have been used as network inputs, as well as 720 data from the daily price of stock options available in the Tehran Stock Exchange market (in 1400) as the network output. The approximate solutions obtained in this article, which were carried out by two methods of neural networks and finite differences on the Tehran stock exchange based on the daily price of stock options, are shown that neural networks are more accurate method comparing with finite difference. The comparison of pricing results using neural networks with real prices in the assumed market is presented and shown via diagram, as well.