http://scholars.ntou.edu.tw/handle/123456789/26812 2026-09-16T11:00:03Z http://scholars.ntou.edu.tw/handle/123456789/26818 標題: Bitcoin volatility forecasting: An artificial differential equation neural network 作者: S. Pourmohammad Azizi; Huang, Chien Yi; Chen, Ti An; Chen, Shu Chuan; Nafei, Amirhossein 摘要: In this article, an alternate method for estimating the volatility parameter of Bitcoin is provided. Specifically, the procedure takes into account historical data. This quality is one of the most critical factors determining the Bitcoin price. The reader will notice an emphasis on historical knowledge throughout the text, with particular attention paid to detail. Following the production of a historical data set for volatility utilizing market data, we will analyze the fundamental and computed values of Bitcoin derivatives (futures), followed by implementing an inverse problem modeling method to obtain a second-order differential equation model for volatility. Because of this, we can accomplish what we set out to do. As a direct result, we will be able to achieve our objective. Following this, the differential equation of the second order will be solved by an artificial neural network that considers the dataset. In conclusion, the results achieved through the utilization of the Python software are given and contrasted with a variety of other research approaches. In addition, this method is determined with alternative ways, and the outcomes of those comparisons are shown. 2023-01-01T00:00:00Z http://scholars.ntou.edu.tw/handle/123456789/26817 標題: A Dynamical Systems Approach to Machine Learning 作者: S. Pourmohammad Azizi; Neisy, Abdolsadeh; Ahmad Waloo, Sajad 摘要: Employing various mathematical tools in machine learning is crucial since it may enhance the learning problem's efficiency. Dynamic systems are among the most effective tools. In this study, an effort is made to examine a kind of machine learning from the perspective of a dynamic system, i.e., we apply it to learning problems whose input data is a time series. Using the discretization approach and radial basis functions, a new data set is created to adapt the data to a dynamic system framework. A discrete dynamic system is modeled as a matrix that, when multiplied by the data of each time, yields the data of the next time, or, in other words, can be used to predict the future value based on the present data, and the gradient descent technique was used to train this matrix. Eventually, using Python software, the efficacy of this approach relative to other machine learning techniques, such as neural networks, was analyzed. 2023-11-01T00:00:00Z http://scholars.ntou.edu.tw/handle/123456789/26816 標題: Inverse Problems to Estimate Market Price of Risk in Catastrophe Bonds 作者: S. Pourmohammad Azizi; Neisy, Abdolsadeh 摘要: This research focuses on evaluating the market price of risk for catastrophe bonds (CAT bonds). Our approach involves constructing a model for CAT bonds that incorporates stochastic process interest rates and losses, followed by numerical methods. Recognizing the inherent challenge of directly obtaining the market price of risk from the market, we utilize inverse problems to derive it. Our assumptions include the CIR stochastic process model for the interest rates and the jump-diffusion stochastic process model for the loss. Through the analysis of a risk-free portfolio, we illustrate the alignment of CAT bonds with partial integral differential equations (PIDE). Employing inverse problems, we then estimate the market price of risk by solving the PIDE. Specifically, we implement Tikhonov regularization and propose a systematic method for determining the market price of risk. 2024-11-01T00:00:00Z http://scholars.ntou.edu.tw/handle/123456789/26815 標題: Inverse Problem Approach to Machine Learning with Application in the Option Price Correction 作者: S. Pourmohammad Azizi; Jafari, Hossein; Faghan, Yaser; Neisy, Abdolsadeh 摘要: We investigate a new method in learning to fix the existence of an unsuitable subfunction of a general system. We assume this subfunction is dependent on the system input variables. In this process, we put a learner instead of the unsuitable subfunction and train it by a training model obtained from inverse problems and fractional derivatives, respectively. Finally, we implemented this method on a simple financial model and examined the results with simulated and real data. 2022-04-01T00:00:00Z