Erfan Salavati

Amirkabir University of Technology | TUS · Department of Mathematics and Computer Science

In this research, three machine learning methods XGBoost, AdaBoost, logistic regression and random forest are used to predict the price of Bitcoin in the next 1 minute. The input variables include a number of technical indicators and information related to the price of Bitcoin from January 1, 2012 to It is March 31, 2021. The main goal of this rese...

The COVID-19 pandemic caused a significant disruption to food demand, leading to changes in household expenditure and consumption patterns. This paper presents a method for analyzing the impact of such demand shocks on a producer’s decision to sell a commodity during economic turmoil. The method uses an artificial neural network (ANN) to approximat...

A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using probabilistic ideas. We discuss non-negative solutions. We also generalize this idea to a class of non-linear parabolic di...

Calibration of multidimensional economic problems proven to be difficult, as there is a high risk of problem miss-identification. In this paper we propose a multi-stage calibration method to estimate the six parameters of a commodity market price model that includes storage. We assume that the commodity prices are derived from the optimal commodity...

In this article, we propose an agent-based model for LOB markets, and by simulation, we estimate the model’s parameters. This model has two interesting points. First, we divide the data transaction of 1 day into six parts. Second, we detect price manipulation by using intraday transaction data. To detect price manipulation, we simulate the model on...

This thesis serves three primary purposes, first of which is to forecast two stocks, i.e. Goldman Sachs (GS) and General Electric (GE). In order to forecast stock prices, we used a long short-term memory (LSTM) model in which we inputted the prices of two other stocks that lie in rather close correlation with GS. Other models such as ARIMA were use...

In this article, we introduce an agent‐based model for a Limit Order Book (LOB) market with a price limit and simulate and estimate its parameters. In this framework, we have reached a linear relation between the percentage of the sellers in the market and the changes in the logarithm of the price. Moreover, we demonstrate that in this model if the...

The sheer size of data in the new age is not only a challenge for computer hardware but also the essential bottleneck for the efficiency of many machine learning algorithms.In this issue, we, describe the difference between factor models and principal component analysis (PCA). Both techniques are utilized to "simplify" complex data sets mainly coll...

A new family of distributions on the circle is introduced which are a generalization of the Cardioid distributions. The elementary properties such as mean, variance and the characteristic function are computed. The distribution is either unimodal or bimodal. The modes are computed. The symmetry of the distribution is characterized. The parameters a...

Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time homogeneous with $\sigma$-finite intensity measure on a metric space. By using finite element methods and Galerkin approximations, some explicit and implicit d...

Black-Litterman is a framework of allowing incorporating investors’ views based on prior information to derive a posterior distribution of portfolio returns and asset allocations. Traditionally, the Bayes estimation of return is calculated using squared error loss function. However, in some situations, loss of overestimation and underestimation of...

It is well known that in the forecasting of a target variable the linear models reduce to single index models, but it is shown by Fan et al. that in nonlinear forecasting models, there is a possibility to extract multiple indices from the factors. In this method, the sufficient factors are identified as the eigenvectors of the conditional covarianc...

It is well known that in the forecasting of a target variable the linear models reduce to single-index models, but it is shown by Fan et al. that in nonlinear forecasting models, there is a possibility to extract multiple indices from the factors. In this method, the sufficient factors are identified as the eigenvectors of the conditional covarianc...

We use a new method developed by Fan et al. (2017) to forecast macroeconomic time series. The main tools of this method are dimension reduction, slicing, and local regression. This method is also applied to cross sectional sufficient regression using extracted factors. We apply this method to the forecasting of several time series derived from Iran...

In this article, we define the new concept of local coupling property for Markov processes and study its relationship with distributional properties of the transition probability. In the special case of L\'evy processes we show that this property is equivalent to the absolute continuity of the transition probability and also provide a sufficient co...

A well-known result on pathwise uniqueness of the solution of stochastic differential equations in R is the Yamada-Watanabe theorem. We have extended this result by replacing the Lipschitz assumption on the drift coefficient by much weaker assumption of semi-monotonicity.

Semilinear stochastic evolution equations with L\'evy noise and monotone nonlinear drift are considered. The existence and uniqueness of the mild solutions in $L^p$ for these equations is proved and a sufficient condition for exponential asymptotic stability of the solutions is derived. The main tool in our study is an It\^o type inequality for the...

An inequality for the $p$th power of the norm of a stochastic convolution integral in a Hilbert space is proved. The inequality is stronger than analogues inequalities in the Literature in the sense that it is pathwise and not in expectation. An application of this inequality is provided for the semilinear stochastic evolution equations with L\'evy...

We consider infinitely divisible distributions with symmetric L\'evy measure and study the absolute continuity of them with respect to the Lebesgue measure. We prove that if $\eta(r)=\int_{|x|\le r} x^2 \nu(dx)$ where $\nu$ is the L\'evy measure, then $\int_0^1 \frac{r}{\eta(r)}dr <\infty$ is a sufficient condition for absolute continuity. As far a...

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differential equations and stochastic dela...

Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients which as far as we know, h...

Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity condition on coefficients. Existence and uniqueness of the mild solution is proved using an iterative method. The continuity of the solution with respect to initial condition a...

This paper introduces a novel coding scheme based on the diffusion map framework. The idea is to run a t-step random walk on the data graph to capture the similarity of a data point to the codebook atoms. By doing this we exploit local similarities extracted from the data structure to obtain a global similarity which takes into account the non-line...