List of articles (by subject) Numerical Methods in Mathematical Finance
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Open Access Article
1 - Estimating Efficiency of Bank Branches by Dynamic Network Data Envelopment Analysis and Artificial Neural Network
Javad Niknafs Mohammad Ali Keramati Jalal HaghighatmonfaredNetwork data envelopment analysis models assess efficiency of decision-making unit and its sections using historical data but fail to measure efficiency of its units and their internal stages in the future. In this paper we aim to measure efficiency of stages of bank br MoreNetwork data envelopment analysis models assess efficiency of decision-making unit and its sections using historical data but fail to measure efficiency of its units and their internal stages in the future. In this paper we aim to measure efficiency of stages of bank branches and obtain efficiency trend of stages during the time, then to estimate their efficiency in the future therefore we can be aware of stages inefficiency before occurrence and prevent them. First, a two-stage structure including deposit collection and loan giving was designed for bank branches using literature review and comments of experts. Human forces and fixed assets were considered as input variables of the first stage, deposit as mediator variable, delayed claims as interim variable, and loan amount as output variable of the second stage. Then, a dynamic network data envelopment analysis model was formulated and stages efficiency were obtained for 16 consecutive periods. Therefore, efficiency trend of stages was obtained during the time. In the following, efficiency of various stages of branches were estimated using artificial neural network and some recommendations are provided according to obtained amounts in order to prevent inefficiency before occurrence. Manuscript profile -
Open Access Article
2 - Identification the Periods of Formation and Bursting of Speculative Bubbles in Iranian Stock Market Using Quantitative Models
Seyed Ali Nabavi Chashmi Mohammad Reza MahjoobThe purpose of this study is to investigate and identify the periods of formation and bursting of speculative bubbles in Iran's capital market by creating a state space model and two-mode switching regime (mode 1 is bubble growth and burst stage and mode 2 is the time o MoreThe purpose of this study is to investigate and identify the periods of formation and bursting of speculative bubbles in Iran's capital market by creating a state space model and two-mode switching regime (mode 1 is bubble growth and burst stage and mode 2 is the time of bubble loss) during the period from April 2011 to March 2018. The Oxmetrics 7 software is used to investigate the existence of multiple bubbles and research objective. The results of the study of the state space switches confirm the bubble of the capital market in Iran during four periods in the research domain. The life span of the first speculative bubble is 2 months from October to November 2011, the second is 8 months from March to October 2013, the third is 3 months from December 2015 to February 2016, and the fourth period of bubble is 5 months from August to December 2017. Therefore, the result of the research stipulates that the stock index of the Iranian capital market in the realm of research time period has had 18 months of bubbles and has spent 66 months in balance. Manuscript profile -
Open Access Article
3 - Numerical Solution of Multidimensional Exponential Levy Equation by Block Pulse Function
Minoo Bakhshmohammadlou Rahman FarnooshThe multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensiona MoreThe multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a Poisson operational matrix. Then we reduce our equation to a linear lower triangular system by constant, Wiener and Poisson operational matrices. Finally using the forward substitution method, we obtain an approximate answer with the convergence rate of O(h). Moreover, we illustrate the accuracy of the proposed method with a 95% confidence interval by some numerical examples.‎ Manuscript profile -
Open Access Article
4 - Investigating the Mathematical Models (TOPSIS, SAW) to Prioritize the Investments in the Accepted Pharmaceutical
Reza JameiConsidering the importance of decision- making in investment, this study prioritizes the accepted pharmaceutical companies in Tehran stock exchange, during 2013-2017 using the following criteria: the return on investment (ROI), reminded increment (RI), return on sales ( MoreConsidering the importance of decision- making in investment, this study prioritizes the accepted pharmaceutical companies in Tehran stock exchange, during 2013-2017 using the following criteria: the return on investment (ROI), reminded increment (RI), return on sales (ROS) and the earnings per share (EPS). Price per earnings ratio of each share (P/E), return on equity (ROE), return on assets (ROA). After prioritization mentioned companies, they were ranked using mathematical models: SAW and TOPSIS. The object of the study is to encourage financial decision- makers to use math models (SAW, TOPSIS) instead of previous accounting techniques in order to represent the pharmaceutical companies more perfect than before. The comparison between ranked mentioned companies' according to two math models (SAW, TOPSIS) showed that there is not a significant deference between ranks obtained from SAW and TOPSIS. Furthermore, it is found out that the ranking of the involved companies' was not the same during the study. Some had better process while others not only didn’t have improvement but also gained worse ranking during the study than before. Manuscript profile -
Open Access Article
5 - A CRITIC-based improved version for multiple criteria ABC inventory classification
Amir MohamadghasemiIn this paper, we present an improved version of the Ramanathan [R. Ramanathan, ABC inventory classification with multiple-criteria using weight linear optimization, Computer and Operations Research, 2006, 33, 695-700] and Zhou and Fan models [P. Zhou and L. Fan, A note MoreIn this paper, we present an improved version of the Ramanathan [R. Ramanathan, ABC inventory classification with multiple-criteria using weight linear optimization, Computer and Operations Research, 2006, 33, 695-700] and Zhou and Fan models [P. Zhou and L. Fan, A note on multi-criteria ABC inventory classification (MCABCIC) using weighted linear optimization, European Journal of Operation Research, 2007, 182, 1488-1491]. The model that Ramanathan [1] offered, hereafter the R-model, in spite of its advantages may be led to a situation in which the weights of some criteria regarding an item would not play any role in determining its overall score. On the other hand, for the R inventory items, the Zhou and Fan [2] approach, hereafter the ZF-model, may be resulted to a situation where an item with the high value for an unimportant criterion is inappropriately classified as class A. Moreover, none of the above studies take into account the ranking order (RO) of criteria. Hence, in order to remove drawbacks of both approaches, an integrated model based on criteria importance through inter-criteria correlation (CRITIC) is applied. At last, the proposed method is implemented in an illustrative example and the results are compared with the others. Manuscript profile -
Open Access Article
6 - Optimization of the Black-Scholes Equation with the Numerical Method of Local Expansion to Minimize Risk Coverage
Amirreza Keyghobadi Shadan Behzadi Fatemeh GerveiIn this paper, we present an efficient and accurate method for calculating the Black-Scholes differential equations and solve the Black-Scholes equations using Jacoby and Airfoil orthogonal bases, with the collocation method. The Black-Scholes equation is a partial diff MoreIn this paper, we present an efficient and accurate method for calculating the Black-Scholes differential equations and solve the Black-Scholes equations using Jacoby and Airfoil orthogonal bases, with the collocation method. The Black-Scholes equation is a partial differential equation, which describes the price of choice in terms of time and the collocation method is a method of deter-mining coefficients. Then we show the computational results and examine the performance of the method for the two options, the price of basic assets and its issues. These results show that the Jacoby method is more efficient in solving the Black Scholes equation, and the method error is less and the convergence rate is higher. In this paper, by applying numerical methods to the desired equation, nonlinear devices can be solved by nonlinear solution methods, such as Newton's iterative method. The existence, uniqueness of the solution, and convergence of the methods are examined, and we will show in an example that by repeating then |u n+1-u n |/|u n | <ε can be reached and this indicates the accuracy of the response to these methods. Manuscript profile -
Open Access Article
7 - Measurement of Bitcoin Daily and Monthly Price Prediction Error Using Grey Model, Back Propagation Artificial Neural Network and Integrated model of Grey Neural Network
Mahdi Madanchi Zaj Mohammad Ebrahim Samavi Emad KooshaOne of the recent financial technologies is Block chain-based currency known as Cryptocurrency that these days because of their unique features has become quite popular. The first known Cryptocurrency in the world is Bitcoin, and since the cryptocurrencies market is a c MoreOne of the recent financial technologies is Block chain-based currency known as Cryptocurrency that these days because of their unique features has become quite popular. The first known Cryptocurrency in the world is Bitcoin, and since the cryptocurrencies market is a contemporary one, Bitcoin is currently considered as the pioneer of this market. Since the value of the previous Bitcoin prices data have a non-linear behaviour, this study aims at predicting Bitcoin price using Grey model, Back Propagation Artificial Neural Network and Integrated Model of Grey Neural Network. Then, the prediction’s accuracy of these methods will be measured using MAPE and RMSE indices and also Bitcoin price data for a five-year period (2014-2018). The results had indicated that wen estimating Bitcoin daily prices, Back Propagation Artificial Neural Network model has the lowest absolute error rate (5.6%) compared to the Grey model and the integrated model. Additionally, for the monthly prediction of Bitcoin price, the integrated model, with the lowest absolute error rate (9%), has a better performance than the two other models. Manuscript profile -
Open Access Article
8 - An anticipating class of Fuzzy Stochastic Differential Equations
Hossein Jafari Hamed Farahani Mahmoud ParipourWe consider a class of fuzzy stochastic differential equations (FSDE), in which the integrands of thestochastic integrals are not adapted to the duration generated by a Wiener process. Such equations with randomness, fuzziness, and non-adapted processes can be applied MoreWe consider a class of fuzzy stochastic differential equations (FSDE), in which the integrands of thestochastic integrals are not adapted to the duration generated by a Wiener process. Such equations with randomness, fuzziness, and non-adapted processes can be applied in financial models. We discuss the existence and uniqueness of strong solutions.We consider a class of fuzzy stochastic differential equations (FSDE), in which the integrands of thestochastic integrals are not adapted to the duration generated by a Wiener process. Such equations with randomness, fuzziness, and non-adapted processes can be applied in financial models. We discuss the existence and uniqueness of strong solutions. Manuscript profile -
Open Access Article
9 - A New Non-monotone Line Search Algorithm to Solve Non-smooth Optimization Finance Problem
Saeed Banimehri Hamid EsmaeiliIn this paper, a new non-monotone line search is used in the diagonal discrete gradient bundle method to solve large-scale non-smooth optimization problems. Non-smooth optimization problems are encountered in many applications in fi-nance problems. The new principle cau MoreIn this paper, a new non-monotone line search is used in the diagonal discrete gradient bundle method to solve large-scale non-smooth optimization problems. Non-smooth optimization problems are encountered in many applications in fi-nance problems. The new principle causes the step in each iteration to be longer, which reduces the number of iterations, evaluations, and the computational time. In other words, the efficiency and performance of the method are improved. We prove that the diagonal discrete gradient bundle method converges with the pro-posed non-monotone line search principle for semi-smooth functions, which are not necessarily differentiable or convex. In addition, the numerical results confirm the efficiency of the proposed correction. Manuscript profile