Journal of mathematic and modeling in Finance
Volume:3 Issue: 2, Summer - Autumn 2023

‎Forecasting price trends in financial markets is of particular importance for traders because price trends are inherently dynamic and forecasting these trends is complicated‎. In this study‎, ‎we present a new hybrid method based on combination of the dynamic mode decomposition method and long short-term memory method for forecasting financial markets‎. This new method is in this way that we first extract the dominant and coherent data using the dynamic mode decomposition method and then predict financial market trends with the help of these data and the long short-term memory method‎.‎ To demonstrate the efficacy of this method‎, ‎we present three practical examples‎: ‎closing price of US Dollar to Iranian Rial‎, ‎closing prices of zob roy Isfahan stock‎, ‎and also closing prices of siman shargh stock‎. ‎These examples exhibit bullish‎, ‎bearish‎, ‎and neutral behaviors‎, ‎respectively‎.‎ It seems that the proposed new method works better in predicting the financial market than the existing long-short-term memory method‎.

‎In this research‎, ‎we investigated the interactive effects between the macroeconomic variables of currency‎, ‎gold‎, ‎and oil on two indicators of total and equal weighted indices considering the importance of correlation between economic variables and stock market indices‎. ‎In this regard‎, ‎the analysis of Pearson correlation and regression coefficients have been used to investigate the existence of an interactive effect among them‎, ‎and a Multi-Layer Perceptron Neural Network (MLP NN) model has been used to simulate this effect‎. ‎The models have been fitted as a time series based on the daily data related to the economic variables and the mentioned indicators during march 2016 to that of 2021‎. ‎Investigating the interactive effects between variables has been done using SPSS statistical software‎, ‎and Artificial Neural Network (ANN) simulation developed in MATLAB programming environment‎. ‎The extracted results indicate the existence of an interactive effect among these economic variables‎. ‎The simulation results show the high ability of ANN in modeling and predicting the total price and equal-weighted indices‎, ‎and this model has been able to make more accurate predictions by considering these interactive effects as well‎.

Forecasting in the financial markets is vital for informed decision-making, risk management, efficient capital allocation, asset valuation, and economic stability. This study thoroughly examines forecasting techniques to predict the 30-day closing prices of APPLE in a select group of 100 prominent companies chosen based on their revenue profiles. list of 100 big Companies published by The Fortune Global 500. The evaluated forecasting methods encompass a broad spectrum of approaches, including Moving Average (MA), Exponential Smoothing, Autoregressive Integrated Moving Average (ARIMA), Simple Linear Regression, Multiple Regression, Decision Trees, Random Forests, Neural Networks, and Support Vector Regression (SVR). The information on the dataset was downloaded from Yahoo Finance, and all methods were evaluated in Python. The MAPE method is used to measure the accuracy of the examined methods. Based on the selected dataset, Our findings reveal that SVR, Simple Linear Regression, Neural Networks, and ARIMA consistently outperform other methods in accurately predicting the 30-day APPLE closing prices. In contrast, the Moving Average method exhibits subpar performance, primarily due to its inherent limitations in accommodating the intricate dynamics of financial data, such as trends, seasonality, and unexpected shocks. In conclusion, this comprehensive analysis enhances our understanding of forecasting techniques and paves the way for more informed and precise decision-making in the ever-evolving realm of financial markets.

An online portfolio selection algorithm has been presented in this research. Online portfolio selection algorithms are concerned with capital allocation to several stocks to maximize the portfolio return over the long run by deciding the optimal portfolio in each period. Despite other online portfolio selection algorithms that follow Kelly's theory of capital growth and only focus on increasing return in the long term, this algorithm uses the beta risk parameter to exploit upside risk while hedging downside risk. This algorithm follows the pattern-matching approach, uses fuzzy clustering in the sample selection step, and the log-optimal objective function along with the transaction cost and considering the beta risk measure in the portfolio optimization step. The implementation of the proposed algorithm in this research on a 10-stock dataset from the NYSE market in the period of December 2021 to December 2022 shows the superiority of this algorithm in terms of return and risk and the overall Sharpe ratio compared to the algorithms proposed previously in the literature on online portfolio selection.

In recent years, cryptocurrency has attracted more attention and is a new option in the economy and the financial sector. The purpose of this study is to the volatility and “herd behavior” of the cryptocurrency, gold, and stock markets in the US. This research is aimed at investor “herd behavior” and how it correlates with the volatility of three assets: the Standard & Poor's 500 indexes, Bitcoin, and gold. Also, A new formula by applying the conditional standard deviation (risk), maximum return, minimum return, and average return to quantify the herding bias is designed in this research. In this study, the generalized autoregressive conditional heteroscedasticity model (GARCH) and the autoregressive moving average model (ARMA) were both employed. Research results show that Bitcoin is 3.3 times as volatile as the S&P 500 and 4.6 times as volatile as gold. The results of this novel equation also show that the herding bias of Bitcoin is more than 26 times higher than the global average and 10 times higher than the S&P 500. Also, it’s important to consider the energy consumption and sustainability of investments when evaluating their long-term viability and risk. In some cases, investments in companies with strong sustainability practices and low carbon footprints may be seen as lower risk. Since Bitcoin relies on a network of computers to validate transactions based on proof of work and it is an energy consumption consensus mechanism, investment in Bitcoin may be seen as a higher risk.

Given the importance of policyholder classification in helping to make a good decision in predicting optimal premiums for actuaries.This paper proposes, first, an optimal construction of policyholder classes. Second, Poisson-negative Binomial mixture regression model is proposed as an alternative to deal with the overdispersion of these classes.The proposed method is unique in that it takes Tunisian data and classifies the insured population based on the K-means approach which is an unsupervised machine learning algorithm. The choice of the model becomes extremely difficult due to the presence of zero mass in one of the classes and the significant degree of overdispersion. For this purpose, we proposed a mixture regression model that leads us to estimate the density of each class and to predict its probability distribution that allows us to understand the underlying properties of our data. In the learning phase, we estimate the values of the model parameters using the Expectation-Maximization algorithm. This allows us to determine the probability of occurrence of each new insured to create the most accurate classification. The goal of using mixed regression is to get as heterogeneous a classification as possible while having a better approximation. The proposed mixed regression model, which uses a number of factors, has been evaluated on different criteria, including mean square error, variance, chi-square test and accuracy. According to the experimental findings on several datasets, the approach can reach an overall accuracy of 80%. Then, the application on real Tunisian data shows the effectiveness of using the mixed regression model.

The present study aims to investigate the effect of corporate irresponsibility on stock price crash risk by emphasizing the moderating role of financial expertise of the audit committee in companies listed on the Tehran Stock Exchange. To estimate the multiple regression model to test the hypothesis, the aforementioned model was used using panel data by the pooled data method in companies listed on the Tehran Stock Exchange and Eviews 9 statistical software was used for statistical analysis. In this research, 150 companies (1050 company-years) were selected to test the research hypothesis between 2014 and 2020. The Levin, Lien and Wu tests were used to test the reliability of research data, the Jarque-Bera test was used to determine the normality of the data, the regression method was used to express the relationship between variables, t-test statistics to test the significance of regression coefficients, and finally the F-test statistic was used to determine the significance of the equation. In general, the results of testing the research hypotheses indicate that corporate irresponsibility has a significant positive effect on stock price crash risk. The results also show that the financial expertise of the audit committee has a significant moderating effect on the relationship between corporate irresponsibility and stock price crash risk. In fact, the financial expertise of the audit committee reduces the positive relationship between corporate irresponsibility and stock price crash risk.

This study examines the dynamics of the Iranian foreign exchange market and its impact on the exchange rate used by traders, and not the official rate in Iran. The study aims to extend Fama's theory of market efficiency and proposes a new model to define the opposite point called "Historical bias". The study applied the ARIMA and Markov switching models and dynamic conditional correlation to measure the speed of information circulation and to investigate the origin of the Iranian foreign exchange market's impact on the trader rate of the Dollar market. The study analyzed the convergence of the Iranian foreign exchange market based on different rates, the exchange rate used by traders, and the official rate and its effect on developing CBDC in Iran. The results of this study show that based on Fama's theory of market efficiency the foreign exchange market in Iran could have a 15% history-oriented bias, which is significant and would be an important problem for the launching of CBDC in Iran.

The substitution hypothesis postulates that various corpo- rate governance forms and dividend disbursements serve as alternatives. Given that transparent information disclosure mitigates agency issues by lessening information asymmetry and fortifying corporate governance, this study aims to explore the influence of Material Information Dis- closure which includes Groups A, B and Other Cases—characterized by their promptitude and significance—on dividends. Examining the period from 2018 to 2021 and encompassing a sample of 173 listed firms from the Tehran Stock Exchange, the findings affirm the substitution hypothesis. Moreover, Board independence is identified as a moderator in the rela- tionship between Material Information Disclosures and dividend. Fur- thermore, the findings indicate that during the Covid-19 period, Group A and Other Cases were more potent factors for dividend reduction than Group B disclosure.

Insurance companies routinely conduct assessments to estimate loss reserves, crucial for anticipating liabilities arising from claim settlements. These estimations are particularly sensitive to the temporal dynamics of claims processing, encompassing the duration from filing to resolution. In this study, advanced cross-sectional regression techniques are employed, leveraging cargo insurance market data to gauge reported loss reserves. The comprehensive model integrates various influencing factors such as written premiums, paid claims, reinsurance issued premiums, inflation rates, and return on investment. Notably, the analysis unveils a non-significant negative association between inflation rates and loss reserves. Additionally, a negative correlation is observed between paid claims and loss reserves, while a statistically significant positive relationship emerges between written premiums and loss reserves, shedding light on intricate patterns within the insurance market.

‎In this article, fuzzy random variables are used to model interest rate uncertainty used in the calculation of whole life insurance premiums, and calculate the effect of this uncertainty on the price of life settlements. The fuzzy results obtained from deterministic and probabilistic pricing approaches have been compared with the results of the stochastic approach. Also, the results have been analyzed for Iran life table, which has been issued to insurance companies since 1400, and for France life table, which was previously used by insurance companies. In addition, since ‎5-year survival probability for each cancers in Iran was lower than in the United States, the probability adjustment coefficient for Iran was higher than that of the United States. In addition, the interval obtained for the fuzzy probability price and the stochastic price for both Iran and France life tables are close to each other. But in most cases, the fuzzy price obtained based on the deterministic approach has a significant distance from the stochastic and fuzzy probability approaches. Also, the findings of the research indicate that the price calculated using the fuzzy deterministic approach for Iran life table is higher than France life table. While the results for fuzzy probabilistic approach and stochastic approach are completely opposite. In the other words, the price calculated for the Iran life table is lower than the France life table. This difference comes from the fact that the adjustment coefficients for ‎these‎ life tables are calculated for each person separately from ‎related‎ life tables.

This study explores the application of dynamic systems for modeling and valuing catastrophe bonds to establish a more intelligent and adaptive approach to determining their volatility parameter. These financial instruments hold significant importance for insurance companies in safeguarding against the risk of insolvency stemming from the escalating frequency and severity of natural disasters worldwide. Employing mathematical principles, this research formulated a pricing partial differential equation and introduced a dynamic system for its resolution. The damage model was assumed to follow a stochastic process, and a radial basis neural network was utilized to estimate the volatility parameter of this stochastic process by leveraging historical data. The study scrutinized the pricing framework of catastrophe bonds related to floods and storms in China, ultimately demonstrating that the proposed methodology proved effective and computationally efficient when contrasted with alternative approaches.