• hendeseh-taliem-ir

    هندسه

    تومان

     

    احتمالا بابلیان و مصریان کهن نخستین کسانی بودند که اصول هندسه را کشف کردند. در مصر هر سال رودخانه نیل طغیان می‌کرد و نواحی اطراف رودخانه را سیل فرا می‌گرفت. این رویداد تمام علایم مرزی میان املاک را از بین می‌‌برد و لازم می‌‌شد دوباره هر کس زمین خود را اندازه‌گیری و مرزبندی کند. مصریان روش علامت‌گذاری زمین‌ها با تیرک و طناب‌ را ابداع کردند. آنها تیرکی را در نقطه‌ای مناسب در زمین فرو می‌‌کردند و تیرک دیگری در جایی دیگر نصب می‌شد و دو تیرک با طنابی که مرز را مشخص می‌‌ساخت به یکدیگر متصل می‌شدند. با دو تیرک دیگر زمین محصور شده و محلی برای کشت یا ساختمان سازی مشخص می‌شد. در آغاز هندسه برپایه دانسته‌های تجربی پراکنده‌ای در مورد طول و زاویه و مساحت و حجم قرار داشت که برای مساحی و ساختمان و نجوم و برخی صنایع دستی لازم می‌شد. بعضی از این دانسته‌ها بسیار پیشرفته بودند مثلا هم مصریان و هم بابلیان قضیه فیثاغورث را ۱۵۰۰ سال قبل از فیثاغورث می‌شناختند. یونانیان دانسته‌های هندسی را مدون کردند و بر پایه‌ای استدلالی قراردادند. برای آنان هندسه مهم‌ترین دانش‌ها بود و موضوع آن را مفاهیم مجردی می‌دانستند که اشکال مادی فقط تقریبی از آن مفاهیم مجرد بود. در سال ۶۰۰ قبل از میلاد مسیح، یک آموزگار اهل ایونیا (که در روزگار ما این بخش را می توان به عنوان طالس ، چند منبع دیگر یا قضیه هندسی را به عنوان استرلالی ثابت کرد کرد. آغازگر هندسه ترسیمی بودجه. فیثاغورث که او ممکن است بتواند ایونیا و بتواند از شاگردان طالس بودجه ای را برای شما فراهم کند که بتواند به عنوان یک مشهور است. امکان او واضع این قضیه وجود ندارد.

  • A new method for solving of a backward stochastic differential[taliem.ir]

    A new method for solving of a backward stochastic differential equations by using a basic functions

    تومان

    In this paper, we purpose a method for numerical solution of a backward stochastic differential equations driven by standard Brownian motion  as follows: { dX X(T (s) = ) =p. f(X(s))ds + g(X(s))dB(s), s [0, T), The method is stated by using the basic functions based on the block  pulse functions. Finally, we show the method has a good degree of accuracy by using some examples.

  • A numerical method for portfolio selection based on Markov[taliemir]

    A numerical method for portfolio selection based on Markov chain approximation

    تومان

    In this paper, A portfolio selection problem is approximated by a Markov chain which is modulated by a continuous-time, finite-state, Markov chain. The main ingredient of the Markov chain approximation is to approximate the wealth process and utility function of original utility optimization problem by a controlled Markov chain. under the convergence of the approximation scheme, Policy iteration methods as to obtain the optimal controls. A numerical example is provided to illustrate the reability of the algorithm.

  • A Survey on exact analytical and numerical solutions of some[taliem.ir]

    A Survey on exact analytical and numerical solutions of some S.D.E.s based on martingale approach and changing variable method

    تومان

    In this paper, we decide to represent analytical and numerical solutions for stochastic differential equations, specially reputed and famous  equations in pricing and investment rate odels. By making martingale process from an arbitrary process in L2(R) space, we infer equations just with stochastic part (drift free). This method could be done by Ito product formula on initial process and an appropriate martingale process,  then we compare simulating method of arising this new equation with other simulating method like as E.M. and Milstein. Another suitable  method is converting S.D.E.s to O.D.E.s whom we try to omit diffusion part of stochastic equation. Afterwards, it could be solved by different numerical methods like as Runge-kutta from fourth order. In this paper, we solve well known equations such as Gampertz diffusion and logistic diffusion by this method. Another powerful one is change of variable method whom we could analysis and survey a well known group of  stochastic equations like as special case of squared radial Langevin process, Cox-Ingersoll-Ross model and Ornstein-Uhlenbeck process. For numerical solution of these stochastic equations, we could apply wiener chaos expansion method whom we have described in other paper.

  • American Options Pricing by Using Stochastic Optimaltaliem.ir]

    American Options Pricing by Using Stochastic Optimal Control Problems

    تومان

    Stochastic optimal control problems frequently occur in Economics and Finance. Dynamic programming method represents the most known method for solving optimal control problems analytically. As analytical solutions for problems of optimal control are not always available, finding an approximate solution is at least the most logical way to solve them. In this paper, we present some of the basic ideas which are in current use for the solution of the dynamic programming equations. Also, based on the Markov chain approximation techniques, a numerical  procedure is constructed for solution of stochastic optimal control problems. We focus on the approximation in value space method. And the Jacobi and Gauss-Seidel relaxation (iterative) methods are discussed. These are fundamental iterative methods which are used in value space approach. Finally, American options pricing are presented as simplest control problem which is called optimal stopping problem.

  • An approximate method to option pricing in the Heston[taliem.ir]

    An approximate method to option pricing in the Heston model

    تومان

    The Heston model is one of the most popular stochastic volatility models for derivatives pricing, and it is a mathematical model describing the evolution of the volatility of an underlying asset. The model proposed by Heston(1993), takes into account non-lognormal distribution of the assets returns, leverage effect and the important mean-reverting property of volatility. In addition, it has a semi-closed form solution for  European options. In this paper by means of classical Itˆ o calculus, we decompose option prices as the sum of the classical Black-Scholes formula.This decomposition allows us to develop first- and second-order approximation formulas for option prices and implied volatilities in the Heston volatility framework, as well as to study their accuracy for short maturities. Moreover, we show that the corresponding approximations for the implied volatility are linear(firstorder approximation) and quadratic(second-order approximation) in the log stock price.

  • An Efficient Numerical Approximation of the American Option[taliem.ir]

    An Efficient Numerical Approximation of the American Option Pricing Problem

    تومان

    This paper deals with developing an efficient numerical approximation of the American option pricing problem as a free boundary problem. The recently introduced artificial boundary conditions of Han and Wu  are also employed. In order to solve the problem, a finite difference  method is applied.  The research has also taken advantage of the numerical approximation of the free boundary near expiry. Comparing the results coming from this method with those of the former methods, this research has been able to increase the accuracy of the commonly used methods.

  • An Introduction to Variable and Feature Selection[taliem.ir]

    An Introduction to Variable and Feature Selection

    تومان

    Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available. These areas include text processing of internet documents, gene expression array analysis, and  combinatorial chemistry. The objective of variable selection is three-fold: improving the prediction performance of the predictors, providing faster and more cost-effective predictors, and providing a better understanding of the underlying process that generated the data. The contributions of this special issue cover a wide range of aspects of such problems: providing a better definition of the objective function, feature construction, feature ranking, multivariate feature selection, efficient search methods, and feature validity assessment methods.

  • Application of Stochastic Differential Games for Optimal[taliem.ir]

    Application of Stochastic Differential Games for Optimal Investment Strategy Selection

    تومان

    In game theory, distinct games are a group of problems related to modeling and conflict analysis in the context of a dynamic system. This problem usually involves two actors, one pursuer, and an escape from conflicting goals. The pursuit dynamics and inventions are modeled by systems of differential equations. Different games are associated with optimal control problems. In an optimal control problem, there is a unit control u (t), and a single criterion for optimization; the differential game theory divides this into two controls u (t), v (t) and two criteria, one for each player. To give Each player tries to control the status of the system to achieve its goal. The system responds to the input of both players. In this paper, a random differential equation is an approach to an optimal risk-based investment problem from an insurer. A continuous simple economy with two investment vehicles, fixed costs and a share, is considered. The insurer risk process by an emission distribution to combine the Poisson risk process. The purpose of the insurer is to select an optimal test case to minimize the risk described by measuring the convex risk of its terminal wealth. The optimal investment problem is then implemented as a zero-contrast differential between the insurer and the market.

  • Application of SVR with Genetic optimization algorithm in urban[taliem.ir]

    Application of SVR with Genetic optimization algorithm in urban traffic flow forecasting

    تومان

    Forecasting of inter-urban traffic flow has been one of the most important issues globally in the research on road traffic congestion. Due to traffic flow forecasting involves a rather complex nonlinear data pattern; there are lots of novel forecasting approaches to improve the forecasting accuracy. This investigation presents a short-term traffic forecasting model which combines the support vector regression (SVR) model with Genetic Optimization algorithms (SVRGA) to forecast inter-urban traffic flow. Additionally, a numerical example is employed to elucidate the forecasting performance of the proposed SVRGA model. Finally the results compare and their performance with time series models.

  • Application of Wavelet method in de-noising option prices[taliem.ir]

    Application of Wavelet method in de-noising option prices

    تومان

    In so much financial time series are known to carry noise, elimination of noise is necessary. Due to multi-scaling property, the wavelet method is very efficient in dealing with noisy data series. In specific, we propose to use the wavelet method to de-noise option prices before estimating the option-implied risk neutral density (RND) and forecasting future option prices. We use of two RNDs estimated from the perturbed prices and the filtered prices to forecast the out-of-sample options, respectively. Moreover, we compare them with the true Black-Scholes option prices. Results of this study show that, through the use of Monte Carlo simulations, the power of the wavelet method in the de-noising of option price data. It is clearly seen that, by de-noising the perturbed option prices using the wavelet method, most of the noise is removed and the wavelet de-noising method is robust to different levels of noise variance.

  • Confidence interval estimation of option prices by using the[taliem.ir]

    Confidence interval estimation of option prices by using the predicted distribution of implied volatility

    تومان

    Many option pricing formulas have been developed to overcome the restrictive assumptions of Black and Scholes models and to give more accurate prices. Most of the methods are focused on a point prediction of option price. In this paper, we propose a method that predicts a distribution of the implied volatility functions by applying a Gaussian process regression and estimating confidence intervals of option prices using the predicted volatility distributions. To verify the performance of the proposed method, we conducted simulations on some model-generated option prices dataand real option market data. The simulation results show that the proposed method performs well with practically meaningful option ranges as well as overcomes the problem of containing negative prices in their predicted confidence intervals by the  previous works.

  • European Option Pricing with Transaction Costs[taliem.ir]

    European Option Pricing with Transaction Costs

    تومان

    This paper deals with the construction of a finite difference scheme for a nonlinear BlackScholes partial differential equation modelling stock option pricing in the realistic case when transaction costs arising in the hedging of portfolios are taken into account. The analysed model is the Barles-Soner one.

  • Evaluation of Two Popular Models of Volatility on Financial Time[taliem.ir]

    Evaluation of Two Popular Models of Volatility on Financial Time Series

    تومان

    In this paper, we evaluate and compare two classes of varying volatility model, GARCH and stochastic volatility (SV) models on financial time  series. In this case, a closed form estimator for a stochastic volatility model and also its asymptotic properties are considered. Akaike  information criterion (AIC) was used to test the adequacy of the models.

  • Finite Difference Methods For Random Partial Differential[taliem.ir]

    Finite Difference Methods For Random Partial Differential Equations

    تومان

    Random partial differential equations (RPDEs) describe the partial differential equations involving random inputs which may be a random variable. In this paper, we focus on the numerical approximation of random parabolic and elliptic partial differential equations. The main properties of deterministic difference methods, i.e. consistency, stability and convergency, are separately developed for the stochastic case. It is shown that the proposed stochastic difference schemes for random parabolic and elliptic equations have these properties.