simulation

This paper compares stochastic models for simulating leveraged Exchange-Traded Funds (LETFs) price paths, focusing on their applications in risk management and option pricing. Using TQQQ (a 3x leveraged ETF tracking NASDAQ-100) as our case study, we evaluate Geometric Brownian Motion (GBM), Generalized Autoregressive Conditional Heteroskedasticity (GARCH), Heston stochastic volatility, Stochastic Volatility with Jumps (SVJD), and propose a novel Multi-Scale Volatility with Jumps (MSVJ) model that captures both fast and slow volatility components. Furthermore, we develop a comprehensive evaluation framework that examines both price and volatility characteristics of the simulated paths against the actual TQQQ data. Our analysis spans different market conditions, including the COVID-19 crash and the 2022 market drawdown. While our proposed MSVJ model excels in capturing volatility dynamics and price range estimation, we find that each model exhibits unique strengths in different aspects of LETFs’ behavior. The choice of most appropriate model depends on specific considerations for different applications, such as risk assessment, options pricing, or portfolio management.

The basic necessities of life are food, shelter and clothing. Food is more necessary because the existence of life depends on food. In order to foster global food security, integrated pest management (IPM), an environmentally-friendly program, was designed to maintain the density of pest population in the equilibrium level below the economic damage. For years, mathematics has been an ample tool to solve and analyze various real-life problems in science, engineering, industry and so on but the use of mathematics to quantify ecological phenomena is relatively new. While efforts have been made to study various methods of pest control, the extent to which pests’ enemies as well as natural treatment can reduce crop damage is new in the literature. Based on this, deterministic mathematical models are designed to investigate the prey-predator dynamics on a hypothetical crop field in the absence or presence of natural treatment. The existence and uniqueness of solutions of the models are examined using Derrick and Grossman’s theorem. The equilibria of the models are derived and the stability analysed following stability principle of differential equations and Bellman and Cooke’s theorem. The theoretical results of the models are justified by a means of numerical simulations based on a set of reasonable hypothetical parameter values. Results from the simulations reveal that the presence of pests’ enemies on a farm without application of natural treatment may not avert massive crop destruction. It is also revealed that the application of natural treatment may not be enough to keep the density of the pest population below the threshold of economic damage unless the rate of application of natural treatment exceeds the growth rate of the pest.

The motive of this paper is to investigate the SEIQRD model of the COVID-19 outbreak in Indonesia with the help of a fractional modeling approach. The model is described by the nonlinear system of six fractional order differential equations (DE) incorporating the Caputo-Fabrizio Fractional derivative (CFFD) operator. The existence and uniqueness of the model are proved by applying the well-known Banach contraction theorem. The reproduction number ($R_0$) is calculated, and its sensitivity analysis is conducted concerning each parameter of the model for the prediction and persistence of the infection. Moreover, the numerical simulation for various fractional orders is performed using the Adams-Bashforth technique to analyze the transmission behavior of disease and to get the approximated solutions. At last, we represent our numerical simulation graphically to illustrate our analytical findings.

The goal of this paper is to study the problem of estimation of varextropy function under $\alpha$-mixing dependence condition. We propose nonparametric estimators for varextropy, residual varextropy and  past varextropy. Asymptotic properties of the proposed estimators  are investigated under regularity conditions. Moreover, the comparison of the proposed estimators for varextropy in terms of the bias and mean squared error has been done by Monte Carlo method. Furthermore, a real data example is presented.

This study presents a model of ‎a quantum dot laser with a planar cavity, employing numerical methods and artificial neural networks for simulation purposes. The investigation focuses on the influence of critical parameters, including the injection current into the active layer of the quantum dot laser and the carrier relaxation time to a lower energy state level. The model delves into the intricate carrier and photon dynamics within the laser, solving a system of coupled equations that describe these interactions. The fourth-order Runge-Kutta method is utilized to solve these equations numerically. ‎‎The results indicate that increased pumping power enhances the stable power levels and the peak power output of the laser. Additionally, analysis of the power versus intensity of current ($P-I$) characteristic curve‎ ‎ reveals that a longer carrier relaxation time to a lower energy state leads to a higher threshold current and a reduction in the quantum efficiency of the device‎. ‎The study also examines the laser switch-on time against the injection current. Finally, the deterioration in the quality of quantum dots and quantum wells is scrutinized‎. To gain deeper insights into the effect of increased pumping current on laser switch-on time‎, ‎the study complements numerical findings with the application of artificial neural networks, yielding significant results.

COVID-19 was declared a pandemic on March 11, 2020, after the global cases and mortalities in more than 100 countries surpassed 100 000 and 3 000, respectively. Because of the role of isolation in disease spread and transmission, a system of differential equations were developed to analyse the effect of isolation on the dynamics of COVID-19. The validity of the model was confirmed by establishing the positivity and boundedness of its solutions. Equilibria analysis was conducted, and both zero and nonzero equilibria were obtained. The effective and basic reproductive ratios were also derived and used to analyze the stability of the equilibria. The disease-free equilibrium is stable both locally and globally if the reproduction number is less than one; otherwise, it is the disease-endemic equilibrium that is stable locally and globally. A numerical simulation was carried out to justify the theoretical results and to visualise the effects of various parameters on the dynamics of the disease. Results from the simulations indicated that COVID-19 incidence and prevalence depended majorly on the effective contact rate and per capita probability of detecting infection at the asymptomatic stage, respectively. The policy implication of the result is that disease surveillance and adequate testing are important to combat pandemics.

Systemic risk is the risk imposed by a financial institution on the entire economy, the importance of which has become clear to many policymakers and economists since the financial crisis of 2008, and its measurement has been put on the agenda of many researchers. The present study presents a combined method of systemic risk measurement, in which the shape of the communication graph and the structural characteristics of financial institutions are simultaneously considered. In the proposed method, first, the communication graph is clustered using the Markov clustering algorithm. Then the systemic risk of each financial institution is measured according to its position in the cluster and using the adjusted semi-local centrality systemic risk measure.  The effectiveness of the proposed method has been investigated for banks registered with the Tehran Stock Exchange and Securities Organization from 2014 to 2018 with monthly periods. Based on the results, the linear correlation of systemic risk changes calculated based on the proposed method with systemic risk calculated through simulation (SIR) was higher than the correlation of systemic risk calculated with $\Delta$CoVaR and PageRank measures. Also, based on the results, Mellat, Trade and Export banks have the highest systemic risk and the lowest systemic risk related to capital, and tourism banks.

In this article, a novel model for the dynamics of toxoplasmosis in human and cat populations with vertical transmission and contribution of oocysts to the environment from the mildly infected cats is constructed. The non-negative properties of the model's solutions are proved. We demonstrate that a secondary quantity that affects the overall dynamics of T. gondii in human and cat populations is the reproductive ratio $\mathcal{R}_{\circ}$. The impact of the contribution of oocysts from the mildly infected cats as well as the impact of vertical transmission and the impact of effective contact between cat and cat and cat and humans on the reproductive ratio are shown. The model's endemic and disease-free equilibria are derived, and their local and global stabilities are proved. The bifurcation and sensitivity of the model's parameters to T. gondii dynamics are studied. Finally, simulations are performed with the aid of the computer-in-built Runge-Kutta package implemented in the software Maple to illustrate the behavior of the model graphically. The results indicate that vertical transmission, contact with the infected cats and the contribution of T. gondii from the mildly infected cats have a significant impact on the dynamics of toxoplasmosis.

Due to the emergence of social networking platforms, a large number of users around the world are being part and partial of this platform. At a fraction of the time users on social media are communicating digital files in the form of text, video, images, voice and music which ultimately generates big data. The matter of interest is to estimate precisely the average file size at time duration (occasion). The time may hours or days or months. This paper presents a sample-based methodology to deal with mean size estimation of digital communication content spreading on a social media platform. An estimator is suggested using a random sample from big data and its properties are derived. A simulation method is suggested that computes the confidence interval (CI) for the prediction of précised range of digital file size. The proposed method produces an optimal confidence interval at the suitable choice of constant. These estimated confidence intervals can be used for developing $\alpha$-control charts for constant monitoring of the growth in file size in social media storage at the data centre. If the growth of mean digital file size crosses the upper limit then additional storage infrastructure is needed at the administration level of the social media site. One can generate machine learning algorithms proposed method for monitoring the growth of average digital file size over time duration.

In this research, the system dynamics method has been used to simulate the causal loop model of the goals of the West from the nuclear dispute with Iran. First, we deal with the crises in which the Western world, the US at its head (especially the US), is involved. In the following, the status of sanctions policy and economic sanctions are discussed as the pressure lever in contrast to political issues and international conflicts. Given the existence of the Iran-West nuclear dispute, and the US at its head (mainly the US), the effects of the sanctions are expressed below and the relationship between the goals of the West and the nuclear dispute with Iran is shown by developing a comprehensive model. In the model, the goals of the West from the nuclear dispute with Iran, including the transition of the West from fossil fuels to new energy, the US trade deficit by raising the price of oil, the systemic leap of the West, the survival of the military industry of the West, and the project of the passageway of Western civilization using causal loops are modeled. The developed models provide a comprehensive and systematic perspective for policymakers.

We derive a deterministic mathematical model that scrutinizes the dy-namics of cholera pathogen carriers and the hygiene consciousness of in-dividuals, before the illness, during its prevalence, and after the disease’s outbreaks. The dynamics can effectively help in curtailing the disease, but its effects had less coverage in the literature. Boundedness of the solu-tion of the model, its existence, and uniqueness are ascertained. Effects of cholera pathogen carriers and hygiene consciousness of individuals in controlling the disease or allowing its further spread are analyzed. The differential transformation method is used to obtain series solutions of the differential equations that make the system of the model. Simulations of the series solutions of the model are carried out and displayed in graphs. The dynamics of the concerned state variables and parameters in the model are interpreted via the obtained graphs. It is observed that higher hygiene consciousness of individuals can drastically reduce catching cholera disease at onset and further spread of its infections in the population, this in turn, shortens the period of cholera epidemic.

Supply Chain Management (SCM) is an integrated system of planning and control of materials and information, including suppliers, manufacturers, distributors, retailers, and customers. Chain performance measurement is an important issue in SCM. Also, given that the information plays a key role in improving supply chain performance, the kind and amount of information sharing should be investigated. In this paper, the effect of information sharing on supply chain performance will be evaluated. In this way, 17 different scenarios of information sharing are defined and ranked using the cross-efficiency method. Finally, values ​​for different scenarios using simulations and Rockwell Software Arena V5 are reported. The obtained results show that the proposed model is quite valid and efficient and can be easily applied to real-world cases.

In this paper, the optimal control problem is applied to Human immunodeficiency viruses (HIV) and Herpes simplex virus type 2 (HSV-2) coinfection model formulated by a system of ordinary differential equations. An optimal control system was performed with the help of the Runge-Kutta forward-backward sweep numerical approximation method. Finally, numerical simulation illustrated that a combination of all controls is the most effective strategy to minimize the disease from the community.

Spatial datasets may contain extreme values and exhibit heavy tails. So, the Gaussianity assumption for the corresponding random field is not reasonable. A sub-Gaussian $\alpha$-stable (SG$\alpha$S) random field may be more suitable as a model for heavy-tailed spatial data. This paper focuses on geostatistical data and presents an algorithm for simulating SG$\alpha$S random fields.

In this work, we present a new mathematical model for the spread of hepatitis C disease in two populations: human population and medical equipment population. Then, we apply the Jacobi wavelets method com-bined with the decoupling and quasi-linearization technique to solve this set of nonlinear differential equations for numerical simulation.

Diabetes mellitus is a global health problem, escalating at a disturbing rate due to unbalanced lifestyles and some underlying health issues. In this work, a system of first-order linear ordinary differential equations as well as numerical simulations were employed to gain insight into the dynamics of the disease. The theoretical outcomeof the analysis was derived in terms of the model parameters while computer simulation was used to assess the behavior of the model in terms of the parameter values. Both the theoretical and numerical studies of the model revealed lifestyles and effective treatment as the parameters to be targeted for effective reduction in both diabetes prevalence and mortality. It is therefore concluded that diabetes prevalence and mortality reduction is a function of adjustment in unbalanced lifestyles as well as improvement in diabetes treatment.

A mathematical model has been introduced for the transmission dynamics of cholera disease by GQ Sun et al. recently. In this study, we add Laplacian and Triangular random effects to this model and analyze the variation of results for both cases. The expectations  and coefficients of variation are compared for the random models and the results are used to comment on the differences and similarities between the effects of these probability distributions. The randomness of the model itself is also investigated through comparison of the random and deterministic outcomes.

We study the independent Jeffreys' prior of the unknown location, scale and skewness parameters of truncated-exponential skew-symmetric distributions(TESSD). We show that this prior is symmetric and improper but it yields a proper posterior distribution for some densities. A simulation study using Monte Carlo methods is presented to compare the efficiency of Bayesian estimators in TESSD with Azzalinis' skew models under square error loss and Linex loss functions.

In this paper, mathematical model of COVID-19 Pandemic is discussed. The positivity, boundedness, and existence of the solutions of the model equations are proved. The Disease-free & endemic equilibrium points are identified. Stability Analysis of the model is done with the concept of Next generation matrix. we investigated that DFEP of the model E_0 is locally asymptotically stable if α≤β+δ+μ & unstable if α>β+δ+μ . It is shown that if reproduction number is less than one, then COVID-19 cases will be reduced in the community. However, if reproduction number is greater than one, then covid-19 continue to persist in the Community. Lastly, numerical simulations are done with DEDiscover 2.6.4. software. It is observed that with Constant treatment, increase or decrease contact rate among persons leads great variation on the basic reproduction number which is directly implies that infection rate plays a vital role on decline or persistence of COVID-19 pandemic.

In the present research, an optimization process was performed in Signoff unit of Saipa Corporation based on the discrete event simulation using a multiple objective function. The required information, including the operation classes (product inspection, adjustment, and reworking), the flow between different workstations, operation times, production cost identification, etc., were extracted from the actual data recorded for March 2018- March 2019 period. For the purpose of simulation, firstly, the model was built using the Arena software and all effective parameters and variables were introduced into the model following the planning of various scenarios. Upon a predetermined number of iterations, the bottleneck was identified and the model was verified. Next, in a primary phase, the OptQuest software was utilized to find the optimal number of workers for minimizing the production costs after 378 iterations (upon satisfaction of an automatic stop criterion), and the result was used as input for a secondary phase where the model was optimized for enhancing the operational capacity of the logistic units upon 303 iterations. Using the results of this research, it was anticipated to achieve 21.6% drop in the number of Operator along with 10% increase in the logistic capacity, 4% reduction in the production costs, and 2% increase in the production rate.