Ross Model Research Articles

A Comparison of the Vasicek and Cox, Ingersoll, and Ross Interest Rate Models in Valuation of Insurance Assets, Liabilities and Surplus

Insurance Company’s cash flows are subjected to the risk of interest rate (C-3 risk). To curb the effect of this risk, Insurance companies normally adopts an interest period model that predicts the movement of the rates of interest. The most common models adopted by the Insurance Companies are the vasicek (1977) model and The Cox, Ingersoll and Ross (1985) Model. These two models are stochastic single period short-rate models; however, they exhibit different assumptions and because of this, the future values of insurance Assets and liabilities are likely to differ when these models are applied to estimate their values. Valuing of Insurance Assets and liabilities, especially in the Kenyan market is very challenging because of the tremendous fluctuations of interest rates as a result of gradual increments of the rate of inflation. In order for insurance companies to correctly value their insurance policies, they need to have a substantive Knowledge of their cash flows. The current valuation methods of insurance assets, liabilities and Surplus based on a stochastic interest rate models do not consider the possibility of occurrence of model risk, and therefore there is a possibility of either under estimating the future values of insurance assets and liabilities or over estimating. In this research paper, Geometric simulation was used to explore the effect of model risk By creating a comparison between The vacisek and the Cox, Ingersoll and Ross interest rate model. First, we evaluated the value of an insurance company’s assets and liabilities by assuming that the interest rate process is followed by the Cox, Ingersoll and Ross model and The vasicek (1977). Model risk arose by the different Values obtained for both the vacisek and the Cox, Ingersoll and Ross model. The results of the simulation showed that the cox, Ingersoll and Ross interest rate model provided a better fit of interest as compared to The Vasicek model.

Model for predicting oil testing fluid rheological parameters of Bohai Bay oilfield in wide temperature and pressure range

The rheological parameters of oil testing fluids play a crucial role in safely conducting oil testing operations, protecting reservoirs, and maintaining wellbore integrity, which are greatly influenced by temperature and pressure. This article conducted rheological experiments on commonly used potassium salt polymer systems and organic salt systems for oil testing fluids in the Bohai Bay Oilfield under 4–200 °C and 30–150 MPa. The experiments revealed the variation of rheological parameters with temperature and pressure. Nine commonly used rheological models were evaluated for their applicability to the two types of oil testing fluids. It was found that the Ross model was suitable for the potassium salt polymer system, while the power-law model was suitable for organic salt oil testing fluids. A new rheological parameter prediction model suitable for wide range of temperature and pressure and different testing fluid systems was proposed based on the optimized results. The average error for the potassium salt polymer system for oil testing fluids was 0.101%, and the error for the organic salt system for oil testing fluids was 0.113%. Both were superior to known rheological models and can meet the requirements of oil testing operations within the wide temperature and pressure range in the Bohai Bay Oilfield.

Reproducibility Report for the Paper "Performance Evaluation of Spintronic-Based Spiking Neural Networks Using Parallel Discrete-Event Simulation"

The examined paper introduces Doryta , a simulator for Spiking Neural Networks (SNN) implemented as a ROSS model. The software artifact is available as part of the paper’s supplemental material and can be accessed via the journal’s website. It is well documented and enhances the overall quality of the paper by providing access to the source code of the Dorytra simulator and necessary scripts to reproduce the results shown in the figure. Using the script, we reproduced all major results presented in the paper. Thus, the paper qualifies for the Artifact Available , the Artifact Evaluated - Reusable , and the Artifact Validated - Results Reproduced badges.

Assessing the accuracy of two steady‐state temperature models for onboard passenger vehicle photovoltaics applications

AbstractWe assess the accuracy of two steady‐state temperature models, namely, Ross and Faiman, in the context of photovoltaics (PV) systems integrated in vehicles. Therefore, we present an analysis of irradiance and temperature data monitored on a PV system on top of a vehicle. Next, we have modeled PV cell temperatures in this PV system, representing onboard vehicle PV systems using the Ross and Faiman model. These models could predict temperatures with a coefficient of determination (R2) in the range of 0.61–0.88 for the Ross model and 0.63–0.93 for the Faiman model. It was observed that the Ross and Faiman model have high errors when instantaneous data are used but become more accurate when averaged to timesteps of greater than 1000–1500 s. The Faiman model's instantaneous response was independent of the variations in the weather conditions, especially wind speed, due to a lack of thermal capacitance term in the model. This study found that the power and energy yield calculations were minimally affected by the errors in temperature predictions. However, a transient model, which includes the thermal mass of the vehicle and PV modules, is necessary for an accurate instantaneous temperature prediction of PV modules in vehicle‐integrated (VIPV) applications.

On testing the changes in trends of stock market index and rates

Calibration of interest rate models benefits from grouping data to homogenous classes. Such an approach is typical in many financial time series. Preliminaries have been developed for Cox–Ingersoll–Ross models but this issue remains an open problem for many more realistic interest rate models. Here we develop such a strategy for general class interest rate and classes are based on p-value thresholds for testing for normality and gamma distributions. We use as the benchmark financial series of Chilean stock market index IPSA (Indice de precios selectivo de acciones) and its log-returns. We also study the relationship between interest rate and the market returns represented by the IPSA indicator, with positive correlation in some lags which reveals some interesting facts in the contrary to the conventional theory.

Possibilities of Predicting Peak Oxygen Consumption in Patients With Chronic Heart Failure According to the 6‑Minute Walk Test

To determine the correlation between the results of the 6-minute walk test (6MWT) and peak oxygen consumption (VO2peak) for populations of patients with chronic heart failure with pronounced clinical and demographic differences; to study a possibility of indirect measurement of VO2peak based on the results of 6MWT using the formulas available from the literature. Two databases were analyzed: 50 patients included in the AEROFIT study (group A), and 31 patients from the Almazov National Medical Research Center (group B). The inclusion criteria were the availability of data from the cardiopulmonary stress test and the 6MWT. The possibility of predicting VO2peak was calculated based on the results of 6MWT using the formulas reported in the literature (L. P. Cahalin et al., 1996; R. M. Ross et al., 2010; R. A. Adedoyin et al., 2010). The predictive accuracy of the models was assessed using the coefficient of determination (R2). The relationship between functional and clinical-demographic indicators was assessed using the Pearson or Spearman correlation analysis. The study groups differed significantly in all parameters, except for the proportion of men and the mean VO2peak. Group B patients were 20 years younger than group A patients, had a lower left ventricular ejection fraction (24.06±7.75 and 41.52±10.48 %, respectively; p<0.001), and covered a 130 m shorter distance in the 6MWT. Despite the absence of a significant difference in VO2peak between groups A and B (13.6 and 13.1 ml / kg / min, respectively; p=0.6581), 61 % of group B patients and 20% of group A belonged to Weber functional class IV. In group A, the 6MWT distance correlated closely with VO2peak (R=0.78; p<0.01) and weakly with age (R=0.4) and body mass index (R=0.3). In group B, the 6MWT distance correlated only with VO2peak (R=0.77; p<0.01). For group A, the R.M. Ross et al. model demonstrated high accuracy in determining the mean VO2peak value with a 0.06% prediction error normalized to measured VO2peak. For group B, none of the models showed satisfactory predictive accuracy. The Ross and Cahalin models showed the best coefficients of determination for groups A and B: Group A, Ross et al. (R2=0.58) and Cahalin et al. (R2=0.59); Group B, Ross et al. (R2=0.59) and Cahalin et al. (R2=0.6). In two groups of patients with a statistically insignificant difference in the mean values of VO2peak, the mean values of 6MWT distance were significantly different, although these indicators correlated closely. The VO2peak prediction models showed satisfactory accuracy for estimation of mean VO2, but poor accuracy for estimation of individual values. A better predictive accuracy is determined by similar clinical and demographic characteristics between the training and testing populations, and likely also by models based on larger, more diversified populations.

Development and Validation of a Teaching Module based on the Traditional Approach of the Japanese Bansho Plan Towards the Mastery of Quadratic Equations

This study is an effort to develop and evaluate the validity of the Bansho Plan-Based Teaching Module to improve students’ Higher Order Thinking Skills (HOTS) mastery of the topic of Quadratic Equations. The interactive module comprises six lesson units to provide students with the opportunity to explore the application of the Quadratic Equations concept in real-life situations. The design, development, and validity evaluation of the module was based on the design and development research approach. The discussion focused on two phases, namely the requirements analysis and the development design. The Morrison, Ross, and Kemp (2007) model consisting of nine components was used to support the module development in the first stage of the current study. Meanwhile, the second stage involved an evaluation of the module’s validity and the implementation of a pilot study. Responses from five Mathematics education experts were analyzed using the Percentage Calculation Method (PCM). The highest mean score for content validity coefficient was obtained by the knowledge level aspect with 0.96. This confirms that the module is in line with the national curriculum, as well as the complexity level of all problems presented in the module is not confusing and the module is capable of applying HOTS to the topic of Quadratic Equations. Furthermore, a reliability test was done on the learning objectives through a pilot study involving thirty students. The results showed that the module obtained a Cronbach’s Alpha coefficient value of 0.915, indicating its good consistency. One major contribution of this study is that it highlights the uniqueness of combining multimedia modules with the traditional approach of the Bansho Plan. It creates an awareness that traditional teaching approaches, such as the Bansho Plan, should not be labelled as outdated, but instead its wisdom needs to be explored and adapted to the demands and needs of 21st century teaching.

Design of a novel intelligent computing framework for predictive solutions of malaria propagation model.

The paper presents an innovative computational framework for predictive solutions for simulating the spread of malaria. The structure incorporates sophisticated computing methods to improve the reliability of predicting malaria outbreaks. The study strives to provide a strong and effective tool for forecasting the propagation of malaria via the use of an AI-based recurrent neural network (RNN). The model is classified into two groups, consisting of humans and mosquitoes. To develop the model, the traditional Ross-Macdonald model is expanded upon, allowing for a more comprehensive analysis of the intricate dynamics at play. To gain a deeper understanding of the extended Ross model, we employ RNN, treating it as an initial value problem involving a system of first-order ordinary differential equations, each representing one of the seven profiles. This method enables us to obtain valuable insights and elucidate the complexities inherent in the propagation of malaria. Mosquitoes and humans constitute the two cohorts encompassed within the exposition of the mathematical dynamical model. Human dynamics are comprised of individuals who are susceptible, exposed, infectious, and in recovery. The mosquito population, on the other hand, is divided into three categories: susceptible, exposed, and infected. For RNN, we used the input of 0 to 300 days with an interval length of 3 days. The evaluation of the precision and accuracy of the methodology is conducted by superimposing the estimated solution onto the numerical solution. In addition, the outcomes obtained from the RNN are examined, including regression analysis, assessment of error autocorrelation, examination of time series response plots, mean square error, error histogram, and absolute error. A reduced mean square error signifies that the model's estimates are more accurate. The result is consistent with acquiring an approximate absolute error close to zero, revealing the efficacy of the suggested strategy. This research presents a novel approach to solving the malaria propagation model using recurrent neural networks. Additionally, it examines the behavior of various profiles under varying initial conditions of the malaria propagation model, which consists of a system of ordinary differential equations.

Projection and Contraction Method for Pricing American Bond Options

In this paper, an effective numerical method is proposed for a linear complementarity problem (LCP) arising in the valuation of American bond options under the Cox–Ingersoll–Ross (CIR) model. Firstly, a variable substitution is used to simplify the linear complementary model. Secondly, the finite difference method is adopted to discretize the simplified model, and an equivalent variational form is obtained. Based on the positive definiteness of the discretized matrix, a projection and contraction method (PCM) is adopted for the resulting discretized variational problem. Finally, numerical experiments highlight the effectiveness and performance of the proposed algorithm.

From Transience to Recurrence for Cox–Ingersoll–Ross Model When b < 0

We consider the Cox–Ingersoll–Ross (CIR) model in time-dependent domains, that is, the CIR process in time-dependent domains reflected at the time-dependent boundary. This is a very meaningful question, as the CIR model is commonly used to describe interest rate models, and interest rates are often artificially set within a time-dependent domain by policy makers. We consider the most fundamental question of recurrence versus transience for normally reflected CIR process with time-dependent domains, and we examine some precise conditions for recurrence versus transience in terms of the growth rates of the boundary. The drift terms and the diffusion terms of the CIR processes in time-dependent domains are carefully provided. In the transience case, we also investigate the last passage time, while in the case of recurrence, we also consider the positive recurrence of the CIR processes in time-dependent domains.

Pricing of Pseudo-Swaps Based on Pseudo-Statistics

The main problem in pricing variance, volatility, and correlation swaps is how to determine the evolution of the stochastic processes for the underlying assets and their volatilities. Thus, sometimes it is simpler to consider pricing of swaps by so-called pseudo-statistics, namely, the pseudo-variance, -covariance, -volatility, and -correlation. The main motivation of this paper is to consider the pricing of swaps based on pseudo-statistics, instead of stochastic models, and to compare this approach with the most popular stochastic volatility model in the Cox–Ingresoll–Ross (CIR) model. Within this paper, we will demonstrate how to value different types of swaps (variance, volatility, covariance, and correlation swaps) using pseudo-statistics (pseudo-variance, pseudo-volatility, pseudo-correlation, and pseudo-covariance). As a result, we will arrive at a method for pricing swaps that does not rely on any stochastic models for a stochastic stock price or stochastic volatility, and instead relies on data/statistics. A data/statistics-based approach to swap pricing is very different from stochastic volatility models such as the Cox–Ingresoll–Ross (CIR) model, which, in comparison, follows a stochastic differential equation. Although there are many other stochastic models that provide an approach to calculating the price of swaps, we will use the CIR model for comparison within this paper, due to the popularity of the CIR model. Therefore, in this paper, we will compare the CIR model approach to pricing swaps to the pseudo-statistic approach to pricing swaps, in order to compare a stochastic model to the data/statistics-based approach to swap pricing that is developed within this paper.

Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model

This paper studies insurance companies’ optimal reinsurance–investment strategy under the stochastic interest rate and stochastic volatility model, taking the HARA utility function as the optimal criterion. It uses arithmetic Brownian motion as a diffusion approximation of the insurer’s surplus process and the variance premium principle to calculate premiums. In this paper, we assume that insurance companies can invest in risk-free assets, risky assets, and zero-coupon bonds, where the Cox–Ingersoll–Ross model describes the dynamic change in stochastic interest rates and the Heston model describes the price process of risky assets. The analytic solution of the optimal reinsurance–investment strategy is deduced by employing related methods from the stochastic optimal control theory, the stochastic analysis theory, and the dynamic programming principle. Finally, the influence of model parameters on the optimal reinsurance–investment strategy is illustrated using numerical examples.

Effect of strand debonding on the shear strength of existing pretensioned PC hollow slab

Pretensioned PC (prestressed concrete) beams experience strand debonding failure at the ultimate loading stage, which leads to bond-loss failure of the beams. To study the effect of strand debonding on the shear strength of pretensioned PC hollow slabs, the existing PC hollow slabs of 19 specimens with spans of 10, 13, 16 and 20 m used in Chinese expressway bridges were loaded to bond-loss failure. The strand slip, bond- loss failure mode and shear strength of 19 specimens and 31 shear tests were analyzed. The test results showed that the angles of the failure diagonal cracks were not consistent with the Ross model. Therefore, a refined model to predict the shear strength subjected to pretensioned PC hollow slabs was developed. Other factors were also considered in the refined shear strength model, including the dowel action of longitudinal reinforcements, the prestressed strand development length and the compression zone height. Compared with the shear failure controlled by strand yielding, the shear strength controlled by strand debonding was decreased by approximately 27 %. The test results showed that the debonding induced bond-loss failure could be described as follows: after the formation of the failure diagonal crack, the strand will clearly slip, and concrete parts on both sides of the failure diagonal crack rotate around the crack tip. Due to the debonding induced bond-loss failure of the pretensioned PC hollow slab, the shear strength could not be improved even by increasing the concrete strength of the compression zone. Finally, the validity of the refined model was verified by 23 test specimens.

Rate of convergence of discretized drift parameters estimators in the Cox–Ingersoll–Ross model

The article is devoted to the drift parameters estimation in the Cox–Ingersoll–Ross model. We obtain the rate of convergence in probability of the maximum likelihood estimators based on the continuous-time estimators. Then we introduce the discrete versions of these estimators and investigate their asymptotic behavior. In particular, we establish the conditions for weak and strong consistency, asymptotic normality, and get the rate of convergence in probability.

Uniform Asymptotic Estimate for the Ruin Probability in a Renewal Risk Model with Cox–Ingersoll–Ross Returns

Consider an insurance risk model with arbitrary dependence structures between the claim sizes. Suppose that the risky investment in the insurer can be established by the Cox–Ingersoll–Ross model. When the claim-size distribution is heavy-tailed, a uniform asymptotic formula for ruin probability is obtained.

A novel stochastic modeling framework for coal production and logistics through options pricing analysis

We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory. The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model. We derive a three-dimensional Fast Fourier Transform (“FFT”) lower bound approximation to value the inherent real optionality and for robustness check, we compare the semi-analytical pricing accuracy with the Monte Carlo simulation. Model parameters are estimated from the historical monthly data, and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross (“CIR”) model.

Optimal portfolio problem for an insurer under mean-variance criteria with jump-diffusion stochastic volatility model

This paper studies an insurer's optimal investment portfolio under the mean-variance criterion. The financial market consists of a riskless bond and a risky asset, and the latter's volatility is random. We are extending the Cox–Ingersoll–Ross (CIR) model to the case with jumps, where it is modeled by a jump-diffusion stochastic differential equation (SDE). We use a Lévy SDE to describe the risk process we have, in which we extend the classic Cramér-Lundberg model to the Lévy process, and additionally introduce the stochastic volatility into this model. We assume that the insurer in question is a mean-variance optimizer. In other words, the decision that this insurer faces is to simultaneously maximize and minimize the mean and variance of his/her terminal wealth by selecting an optimal portfolio. We have uncovered closed-form solutions to the mean-variance problem with respect to the efficient strategy and efficient frontier by solving for expected utility maximization of a quadratic function through the martingale method. Finally, we give a numerical example that analyzes the economic behavior of the efficient frontier.

Parameter estimation for discretely observed Cox–Ingersoll–Ross model driven by fractional Lévy processes

<abstract> <p>This paper deals with least squares estimation for the Cox–Ingersoll–Ross model with fractional Lévy noise from discrete observations. The contrast function is given to obtain the least squares estimators. The consistency and asymptotic distribution of estimators are derived when a small dispersion coefficient $\varepsilon \to 0$, $n \to \infty $, $\varepsilon {n^{\frac{1}{2} - d}} \to 0$, and $n\varepsilon \to \infty $ simultaneously.</p> </abstract>

Effect of Solid Concentration and Particle Size on the Flotation Kinetics and Entrainment of Quartz and Hematite

Despite the importance of solid concentration in froth flotation, its effect on flotation kinetics and entrainment has rarely been studied. In this study, the flotation kinetics and entrainment in quartz and hematite single-mineral flotation systems as a function of the solid concentration and particle size were investigated using dodecylamine acetate as a collector. Kinetics modeling showed that the Gamma distribution achieved the best agreement with the experimental data, whereas the Classical and Klimpel models poorly fit the data (e.g., RMSE). The flotation rate constants (k) of both quartz and hematite at a higher solid concentration showed a concave shape, with the inflexion point at the middle-size range, whereas this trend altered at lower solid concentrations. Overall, quartz exhibited higher equilibrium recoveries (R∞) than hematite, which indicates its better overall rate constants. The degree of water recovery in both the quartz and hematite systems was higher at higher solid concentrations, but the hematite system exhibited higher water R∞ than the quartz system, meaning that the entrainment of gangue could be higher in direct hematite flotation than the reverse one. Therefore, a higher solid concentration is associated with better overall quartz recovery and can reduce hematite loss by entrainment during reverse flotation. An inverse relationship was identified between the solid concentration and particle size in terms of the ratio of water recovery to the concentrate. In the reverse flotation of iron ore, refraining from achieving equilibrium recovery could help limit entrainment, but this was not necessarily the case in direct flotation. No entrainment model or method other than the Warren and Ross model approximated the overall trends of flotation at the finest size range (−38 µm). However, extending the Warren method to polynomial distribution led to an improved fit with the experimental results. In addition to the solid concentration, particle density and size were revealed to be key to developing new entrainment models. Finally, after the fast recovery period (true flotation) was over, the slow recoveries were mainly driven by the slow-floating water fraction.

Some qualitative properties of the discrete models for malaria propagation

This paper addresses a reliable mathematical modeling of malaria propagation in infected societies for humans and mosquitoes with an extension of the basic Ross–Macdonald model. We analyze the extended Ross model numerically which is an initial value problem of a seven-dimensional system of the first-order ODEs. For this aim, the discretized scheme of the extended model is split into two parts. First, we apply the step-size functions to approximate the time derivatives with the first-order consistency. Then we use a nonlocal discretization of the standard θ-method to the right side of the system to obtain a linear system. We find the conditions for the step-size functions under which specific intervals are positively invariant for the total populations and each component of the solution of the extended Ross model. We suggest a step-size function for the extended Ross model to preserve the dynamical consistency of the model for any step size Δt. The numerical simulations confirm the theoretical results for the examples and we compare the efficiency of the nonstandard Runge–Kutta methods with the different step-size functions for sufficiently large step sizes.