جستجوی مقالات مرتبط با کلیدواژه « Stochastic differential equations » در نشریات گروه « ریاضی »

In this paper we use stochastic differential equation for estimating the long run equilibrium of the stock prices, the speed of reverting to the mean of the stock prices and the half-life of the stock prices of the selected firms (about 24 active firms) in Tehran Stock Exchange. We use the stock price data of the selected firms to see if the stock prices of these firms have Unit roots tests. For firms which their stock prices are stationary, without unit roots, we follow an Ornstein-Uhlenbeck stochastic differential equation to estimate the half-life of the stock returns of the selected firm. For firms which their stock prices have got the unit root, we use Geometric Brownian Motion for estimation. The results show that most of the studied companies have a reversible behavior to a long-term average and a half-life of stock prices is estimated to be from 3 to 30 weeks. The estimation of the half-life of the stock prices of the selected firms will provide valuable information for the investors and other agents active in the stock markets.

In the list of possible scapegoats for the recent financial crises‎, ‎mathematics‎, ‎in particular mathematical finance has been ranked‎, ‎without‎ ‎a doubt‎, ‎as the first among many and quants‎, ‎as mathematicians are known in the industry‎, ‎have been blamed for developing and using‎‎esoteric models which are believed to have caused the deepening of the financial crisis‎. ‎However‎, ‎as Lo and Mueller (2010) state “Blaming‎‎quantitative models for the crisis seems particularly perverse‎, ‎and akin to blaming arithmetic and the real number system for accounting‎‎fraud.” Throughout the history‎, ‎mathematics and finance have always been in a close relationship‎. ‎Starting from Babylonians‎, ‎through‎‎Thales‎, ‎and then Fibonacci‎, ‎Pascal‎, ‎Fermat‎, ‎Bernoulli‎, ‎Bachelier‎, ‎Wiener‎, ‎Kolmogorov‎, ‎Ito‎, ‎Markowitz‎, ‎Black‎, ‎Scholes‎, ‎Merton and many‎‎others made huge contributions to the development of mathematics while trying to solve finance problems‎. ‎In this paper‎, ‎we present a brief‎‎historical perspective on how the development of finance theory has influenced and in turn been influenced by the development of mathematical‎‎finance theory.

The main purpose of this paper is to provide a quantitative analysis to investigate the behavior of the OPEC oil price. Obtaining the best mathematical equation to describe the price and volatility of oil has a great importance. Stochastic differential equations are one of the best models to determine the oil price, because they include the random factor which can apply the effect of different economical and political elements .In order to earn the best model, at first we study the effectiveness of different stochastic differential equations models and then using the daily OPEC oil price in years 2003 to 2016, according to the high oscillation of oil price due to the various economical and political creases, we divide the data to four parts and estimate the unknown parameters of the equations in these time periods using the General Method of Moment. At last, the best model can be defined by attention to the main price chart and numerical simulations.

Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cannot be considered as the observations in Euclidean spaces due to the various features such as the periodicity of the data. Hence, we cannot analyze them using the common mathematical methods available in Euclidean spaces. In addition, studying and analyzing them using common linear statistics are not possible. One of these typical data is the dihedral angles that are utilized in identifying, modeling and predicting the proteins backbones. Because these angles are representatives of points on the surface of torus, it seems that proper statistical modeling of diffusion processes on the torus could be of a great help for the research activities on dynamic molecular simulations in predicting the proteins backbones. In this article, using the Riemannian distance on the torus, the stochastic differential equations to describe the Brownian motions and Ornstein-Uhlenbeck processes on this geometrical object were derived. Then, in order to evaluate the proposed models, the statistical simulations were performed using the equilibrium distributions of aforementioned stochastic processes. Moreover, the link between the gained results with the available concepts in the non-linear statistics were highlighted.