The methods adopted by static physics corroborating the existence of electromagnetic forces are applicable to the theory of financial markets. Perceived from a classically physical angle, the financial market is defin...The methods adopted by static physics corroborating the existence of electromagnetic forces are applicable to the theory of financial markets. Perceived from a classically physical angle, the financial market is defined as a system composed of several individual entries cooperating upon electromagnetic principles. The approach concerned gives rise to a certain model of financial market, otherwise known as a minority game. In the case of minority game, the allocation of securities and funds is conditioned exclusively upon the fluctuation of prices, where a higher tendency to purchase goods and stocks results in the scale being more profitable and vice versa. Thus players from a minority group gain a prevailing position.展开更多
The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability mean...The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability means that a specific“no-arbitrage”property is unaffected by small(with respect to the Pompeiu–Hausdorff metric)perturbations of the model’s dynamics.We formulate,based on our economic interpretation,a new requirement concerning“no arbitrage”properties,which we call the“uncertainty principle”.This principle in the case of no-trading constraints is equivalent to structural stability.We demonstrate that structural stability is essential for a correct model approximation(which is used in our numerical method for superhedging price computation).We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.展开更多
The digital wave is reshaping the global economic landscape with unprecedented force,especially in the dynamic and promising ASEAN region.Southeast Asia,a multicultural gathering place composed of ten countries,is exp...The digital wave is reshaping the global economic landscape with unprecedented force,especially in the dynamic and promising ASEAN region.Southeast Asia,a multicultural gathering place composed of ten countries,is experiencing profound changes due to the digital revolution,and its marketing model is also displaying new vitality.With soaring internet penetration,widespread use of smartphones,and the booming rise of social media,ASEAN markets have become at the forefront of global digital marketing innovation.This transformation is not only about the application of technology but also involves a comprehensive shift in thinking,consumer behavior,and business strategy.The purpose of this paper is to explore in depth how ASEAN marketing models are innovating in this era and to identify future trends,with a view to providing insights for companies to help them remain competitive in the rapidly changing market.展开更多
This study utilizes the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model to investigate the dynamic relationship between Chinese and U.S. stock markets amid t...This study utilizes the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model to investigate the dynamic relationship between Chinese and U.S. stock markets amid the COVID-19 pandemic. Initially, a univariate GARCH model is developed to derive residual sequences, which are then used to estimate the DCC model parameters. The research reveals a significant rise in the interconnection between the Chinese and U.S. stock markets during the pandemic. The S&P 500 index displayed higher sensitivity and greater volatility in response to the pandemic, whereas the CSI 300 index showed superior resilience and stability. Analysis and model estimation suggest that the market’s dependence on historical data has intensified and its sensitivity to recent shocks has heightened. Predictions from the model indicate increased market volatility during the pandemic. While the model is proficient in capturing market trends, there remains potential for enhancing the accuracy of specific volatility predictions. The study proposes recommendations for policymakers and investors, highlighting the importance of improved cooperation in international financial market regulation and investor education.展开更多
Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ...Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.展开更多
Starting with the self-organized evolution of the trader group’s structure, a parsimonious percolation model for stock market is established, which can be considered as a kind of betterment of the Cont-Bouchaud model...Starting with the self-organized evolution of the trader group’s structure, a parsimonious percolation model for stock market is established, which can be considered as a kind of betterment of the Cont-Bouchaud model. The return distribution of the present model obeys Lévy form in the center and displays fat-tail property, in accord with the styl-ized facts observed in real-life financial time series. Fur-thermore, this model reveals the power-law relationship be-tween the peak value of the probability distribution and the time scales, in agreement with the empirical studies on the Hang Seng Index.展开更多
We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the M...We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors: broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.展开更多
Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure ri...Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.展开更多
The function of E-commerce is becoming more and more widely applied to many fields,which bring about some new challenges and opportunities for the construction of marketing model.It is proved that the more E-com- merc...The function of E-commerce is becoming more and more widely applied to many fields,which bring about some new challenges and opportunities for the construction of marketing model.It is proved that the more E-com- merce applied to the construction of marketing,the more precision of forecast for the enterprises can acquire,which is very helpful for the production and marketing of enterprises.Therefore,the research on the E-commerce applied to the construction of marketing is popular today.This paper applie...展开更多
This paper presents and analyses the internal and external efficiencies of equipment maintenance, and presents that the objective of maintenance is the maximum external efficiency. It defines generalized reliability d...This paper presents and analyses the internal and external efficiencies of equipment maintenance, and presents that the objective of maintenance is the maximum external efficiency. It defines generalized reliability degree of equipment and deduces the correspondent calculating method. It overcomes the defect that traditional calculating method of reliability degree has, which only considers the factor of time not function, therefore we establish a market decision model of equipment maintenance based on it. This model can determine the marginal efficiency of maintenance investment and critical value of generalized reliability degree when it reaches break-even point. After combining the equipment maintenance with economical benefit of enterprise and marketing situation of products, an optimal maintenance strategy will be got. It provides a new method for scientific and rational decisions of equipment maintenance.展开更多
The marketing share model of price and advertising in a duopoly market was studied in this paper. Market response curves of price and advertising were presented to calculate the reasonable range based on the market fo...The marketing share model of price and advertising in a duopoly market was studied in this paper. Market response curves of price and advertising were presented to calculate the reasonable range based on the market forecast results. The interaction effect of price and advertising was considered,and the game theory was applied to a two-stage price and advertising competition which involved the market share model. A marketing decision support system (MDSS) was developed and simulation data was provided to give the solutions. The operation results show that the leading enterprise makes higher price,spends more on advertising,and earns more profit,while the small-scale enterprise has to lower the price,spend less on advertising,and has slightly higher profit rate. The system is shown to be adaptable to a wide variety of realistic situations.展开更多
In order to overcome the shortcomings brought up by the single-layer agency relation analyses of agency problems within enterprise group, two-tiered agency models in the internal capital market are set up, and how ren...In order to overcome the shortcomings brought up by the single-layer agency relation analyses of agency problems within enterprise group, two-tiered agency models in the internal capital market are set up, and how rent-seeking behaviors of member firms' managers affect investment allocation decision made by headquarters manager is demonstrated. From equilibrium solutions of the model, it's inferred that the larger the divergence of member firm's productivity is, the higher probability of investment allocation distortion is.展开更多
In a competitive environment reactive power management is an essential service provided by independent system operator taking into account the voltage security and transmission losses. The system operator adopts a tra...In a competitive environment reactive power management is an essential service provided by independent system operator taking into account the voltage security and transmission losses. The system operator adopts a transparent and non-dis-criminatory procedure to procure the reactive power supply for optimal deployment in the system. Since generators’ are the main source of reactive power generation and the cost of the reactive power should be considered for their noticeable impact on both real and reactive power marginal prices. In this paper, a method based on marginal cost theory is presented for locational marginal prices calculation for real and reactive power considering different reactive power cost models of generators’ reactive support. With the presence of FACTS controllers in the system for more flexible operation, their impact on nodal prices can not be ignored for wheeling cost determination and has also to be considered taking their cost function into account. The results have been obtained for hybrid electricity market model and results have also been computed for pool model for comparison. Mixed Integer Non-linear programming (MINLP) approach has been formulated for solving the complex problem with MATLAB and GAMS interfacing. The proposed approach has been tested on IEEE 24-bus Reliability Test System (RTS).展开更多
In recent years, the speed of urban development becomes faster and faster with expanding of land construction scale, and a lot of idle lands lead to serious land waste. This paper builds game model by carrying out a m...In recent years, the speed of urban development becomes faster and faster with expanding of land construction scale, and a lot of idle lands lead to serious land waste. This paper builds game model by carrying out a market allocation analysis and applying economic game theory to the analysis of current idle land problem; it gets six kinds of results through analyzing the game model of idle land market, and the final Nash equilibrium is(system innovation, publicly traded) through contrastive to help balance the game relationship between government and the user of idle land and raise some new scientific and rational institutions to serve as future references for effective usage of idle land.展开更多
At present,one of the important contents of China s rural land system reform is to build a unified construction land market in urban and rural areas.The unified construction land market in urban and rural areas will p...At present,one of the important contents of China s rural land system reform is to build a unified construction land market in urban and rural areas.The unified construction land market in urban and rural areas will produce higher economic and social benefits.It is imperative to promote the integration of urban and rural construction land market to improve the income of farmers,invigorate the stock of rural collective construction land and improve the efficiency of land use.This paper analyzes the current situation of urban and rural construction land market,the two models and typical cases of urban and rural construction land market integration,the restrictive factors and practical difficulties of urban and rural construction land market integration,and puts forward some suggestions and measures.This provides a theoretical basis for accelerating the integration of urban and rural construction land market,and hopes to provide a certain reference for the integration of urban and rural construction land market.展开更多
This paper examines the forecasting performance of different kinds of GARCH model (GRACH, EGARCH, TARCH and APARCH) under the Normal, Student-t and Generalized error distributional assumption. We compare the effect ...This paper examines the forecasting performance of different kinds of GARCH model (GRACH, EGARCH, TARCH and APARCH) under the Normal, Student-t and Generalized error distributional assumption. We compare the effect of different distributional assumption on the GARCH models. The data we analyze are the daily stocks indexes for Shenzhen Stock Exchange (SSE) in China from April 3^rd, 1991 to April 14^th, 2005. We find that improvements of the overall estimation are achieved when asymmetric GARCH models are used with student-t distribution and generalized error distribution. Moreover, it is found that TARCH and GARCH models give better forecasting performance than EGARCH and APARCH models. In forecasting performance, the model under normal distribution gives more accurate forecasting performance than non-normal densities and generalized error distributions clearly outperform the student-t densities in case of SSE.展开更多
In power market, electricity price forecasting provides significant information which can help the electricity market participants to prepare corresponding bidding strategies to maximize their profits. This paper intr...In power market, electricity price forecasting provides significant information which can help the electricity market participants to prepare corresponding bidding strategies to maximize their profits. This paper introduces the models of autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) which are applied to the price forecasts for up to 3 steps 8 weeks ahead in the UK electricity market. The half hourly data of historical prices are obtained from UK Reference Price Data from March 22nd to July 14th 2010 and the predictions are derived from a sliding training window with a length of 8 weeks. The ARIMA with various AR and MA orders and the ANN with different numbers of delays and neurons have been established and compared in terms of the root mean square errors (RMSEs) of price forecasts. The experimental results illustrate that the ARIMA (4,1,2) model gives greater improvement over persistence than the ANN (20 neurons, 4 delays) model.展开更多
This paper deals with an extension of the one-period model in non-life insurance markets (cf. [1]) by using a transition probability matrix depending on some economic factors. We introduce a multi-period model and in ...This paper deals with an extension of the one-period model in non-life insurance markets (cf. [1]) by using a transition probability matrix depending on some economic factors. We introduce a multi-period model and in each period the solvency constraints will be updated. Moreover, the model has the inactive state including some uninsured population. Similar results on the existence of premium equilibrium and sensitivity analysis for this model are presented and illustrated by numerical results.展开更多
文摘The methods adopted by static physics corroborating the existence of electromagnetic forces are applicable to the theory of financial markets. Perceived from a classically physical angle, the financial market is defined as a system composed of several individual entries cooperating upon electromagnetic principles. The approach concerned gives rise to a certain model of financial market, otherwise known as a minority game. In the case of minority game, the allocation of securities and funds is conditioned exclusively upon the fluctuation of prices, where a higher tendency to purchase goods and stocks results in the scale being more profitable and vice versa. Thus players from a minority group gain a prevailing position.
基金This work is supported by the 863 High-Tcch Project (No. 2004AA104340), the National Natural Science Foundation of China (No. 60173026) and SEC E-Institute: Shanghai High Institutions Grid (No. 200301-1).
文摘The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability means that a specific“no-arbitrage”property is unaffected by small(with respect to the Pompeiu–Hausdorff metric)perturbations of the model’s dynamics.We formulate,based on our economic interpretation,a new requirement concerning“no arbitrage”properties,which we call the“uncertainty principle”.This principle in the case of no-trading constraints is equivalent to structural stability.We demonstrate that structural stability is essential for a correct model approximation(which is used in our numerical method for superhedging price computation).We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.
文摘The digital wave is reshaping the global economic landscape with unprecedented force,especially in the dynamic and promising ASEAN region.Southeast Asia,a multicultural gathering place composed of ten countries,is experiencing profound changes due to the digital revolution,and its marketing model is also displaying new vitality.With soaring internet penetration,widespread use of smartphones,and the booming rise of social media,ASEAN markets have become at the forefront of global digital marketing innovation.This transformation is not only about the application of technology but also involves a comprehensive shift in thinking,consumer behavior,and business strategy.The purpose of this paper is to explore in depth how ASEAN marketing models are innovating in this era and to identify future trends,with a view to providing insights for companies to help them remain competitive in the rapidly changing market.
文摘This study utilizes the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model to investigate the dynamic relationship between Chinese and U.S. stock markets amid the COVID-19 pandemic. Initially, a univariate GARCH model is developed to derive residual sequences, which are then used to estimate the DCC model parameters. The research reveals a significant rise in the interconnection between the Chinese and U.S. stock markets during the pandemic. The S&P 500 index displayed higher sensitivity and greater volatility in response to the pandemic, whereas the CSI 300 index showed superior resilience and stability. Analysis and model estimation suggest that the market’s dependence on historical data has intensified and its sensitivity to recent shocks has heightened. Predictions from the model indicate increased market volatility during the pandemic. While the model is proficient in capturing market trends, there remains potential for enhancing the accuracy of specific volatility predictions. The study proposes recommendations for policymakers and investors, highlighting the importance of improved cooperation in international financial market regulation and investor education.
文摘Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.
基金Th is work was supported by the National Natural Science Foundation of China (Grant Nos. 70171053. 70271070,70471033& 10472ll61)the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP No.20020358009) the Foundation for Graduate Students of University of Science and Tech—nology of China(Grant No.KD 200408).
文摘Starting with the self-organized evolution of the trader group’s structure, a parsimonious percolation model for stock market is established, which can be considered as a kind of betterment of the Cont-Bouchaud model. The return distribution of the present model obeys Lévy form in the center and displays fat-tail property, in accord with the styl-ized facts observed in real-life financial time series. Fur-thermore, this model reveals the power-law relationship be-tween the peak value of the probability distribution and the time scales, in agreement with the empirical studies on the Hang Seng Index.
基金Supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars of State Education Ministry
文摘We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors: broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.
基金Supported by the NNSF of China(40675023)the PHD Foundation of Guangxi Normal University.
文摘Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.
基金This research was supported by the National Social Sci-ence Foundation of China under Grant 06CJL019.
文摘The function of E-commerce is becoming more and more widely applied to many fields,which bring about some new challenges and opportunities for the construction of marketing model.It is proved that the more E-com- merce applied to the construction of marketing,the more precision of forecast for the enterprises can acquire,which is very helpful for the production and marketing of enterprises.Therefore,the research on the E-commerce applied to the construction of marketing is popular today.This paper applie...
文摘This paper presents and analyses the internal and external efficiencies of equipment maintenance, and presents that the objective of maintenance is the maximum external efficiency. It defines generalized reliability degree of equipment and deduces the correspondent calculating method. It overcomes the defect that traditional calculating method of reliability degree has, which only considers the factor of time not function, therefore we establish a market decision model of equipment maintenance based on it. This model can determine the marginal efficiency of maintenance investment and critical value of generalized reliability degree when it reaches break-even point. After combining the equipment maintenance with economical benefit of enterprise and marketing situation of products, an optimal maintenance strategy will be got. It provides a new method for scientific and rational decisions of equipment maintenance.
文摘The marketing share model of price and advertising in a duopoly market was studied in this paper. Market response curves of price and advertising were presented to calculate the reasonable range based on the market forecast results. The interaction effect of price and advertising was considered,and the game theory was applied to a two-stage price and advertising competition which involved the market share model. A marketing decision support system (MDSS) was developed and simulation data was provided to give the solutions. The operation results show that the leading enterprise makes higher price,spends more on advertising,and earns more profit,while the small-scale enterprise has to lower the price,spend less on advertising,and has slightly higher profit rate. The system is shown to be adaptable to a wide variety of realistic situations.
文摘In order to overcome the shortcomings brought up by the single-layer agency relation analyses of agency problems within enterprise group, two-tiered agency models in the internal capital market are set up, and how rent-seeking behaviors of member firms' managers affect investment allocation decision made by headquarters manager is demonstrated. From equilibrium solutions of the model, it's inferred that the larger the divergence of member firm's productivity is, the higher probability of investment allocation distortion is.
文摘In a competitive environment reactive power management is an essential service provided by independent system operator taking into account the voltage security and transmission losses. The system operator adopts a transparent and non-dis-criminatory procedure to procure the reactive power supply for optimal deployment in the system. Since generators’ are the main source of reactive power generation and the cost of the reactive power should be considered for their noticeable impact on both real and reactive power marginal prices. In this paper, a method based on marginal cost theory is presented for locational marginal prices calculation for real and reactive power considering different reactive power cost models of generators’ reactive support. With the presence of FACTS controllers in the system for more flexible operation, their impact on nodal prices can not be ignored for wheeling cost determination and has also to be considered taking their cost function into account. The results have been obtained for hybrid electricity market model and results have also been computed for pool model for comparison. Mixed Integer Non-linear programming (MINLP) approach has been formulated for solving the complex problem with MATLAB and GAMS interfacing. The proposed approach has been tested on IEEE 24-bus Reliability Test System (RTS).
基金Supported by Chinese Tobacco Science and Technology Project(YATAS-KJ-040)
文摘In recent years, the speed of urban development becomes faster and faster with expanding of land construction scale, and a lot of idle lands lead to serious land waste. This paper builds game model by carrying out a market allocation analysis and applying economic game theory to the analysis of current idle land problem; it gets six kinds of results through analyzing the game model of idle land market, and the final Nash equilibrium is(system innovation, publicly traded) through contrastive to help balance the game relationship between government and the user of idle land and raise some new scientific and rational institutions to serve as future references for effective usage of idle land.
文摘At present,one of the important contents of China s rural land system reform is to build a unified construction land market in urban and rural areas.The unified construction land market in urban and rural areas will produce higher economic and social benefits.It is imperative to promote the integration of urban and rural construction land market to improve the income of farmers,invigorate the stock of rural collective construction land and improve the efficiency of land use.This paper analyzes the current situation of urban and rural construction land market,the two models and typical cases of urban and rural construction land market integration,the restrictive factors and practical difficulties of urban and rural construction land market integration,and puts forward some suggestions and measures.This provides a theoretical basis for accelerating the integration of urban and rural construction land market,and hopes to provide a certain reference for the integration of urban and rural construction land market.
文摘This paper examines the forecasting performance of different kinds of GARCH model (GRACH, EGARCH, TARCH and APARCH) under the Normal, Student-t and Generalized error distributional assumption. We compare the effect of different distributional assumption on the GARCH models. The data we analyze are the daily stocks indexes for Shenzhen Stock Exchange (SSE) in China from April 3^rd, 1991 to April 14^th, 2005. We find that improvements of the overall estimation are achieved when asymmetric GARCH models are used with student-t distribution and generalized error distribution. Moreover, it is found that TARCH and GARCH models give better forecasting performance than EGARCH and APARCH models. In forecasting performance, the model under normal distribution gives more accurate forecasting performance than non-normal densities and generalized error distributions clearly outperform the student-t densities in case of SSE.
文摘In power market, electricity price forecasting provides significant information which can help the electricity market participants to prepare corresponding bidding strategies to maximize their profits. This paper introduces the models of autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) which are applied to the price forecasts for up to 3 steps 8 weeks ahead in the UK electricity market. The half hourly data of historical prices are obtained from UK Reference Price Data from March 22nd to July 14th 2010 and the predictions are derived from a sliding training window with a length of 8 weeks. The ARIMA with various AR and MA orders and the ANN with different numbers of delays and neurons have been established and compared in terms of the root mean square errors (RMSEs) of price forecasts. The experimental results illustrate that the ARIMA (4,1,2) model gives greater improvement over persistence than the ANN (20 neurons, 4 delays) model.
文摘This paper deals with an extension of the one-period model in non-life insurance markets (cf. [1]) by using a transition probability matrix depending on some economic factors. We introduce a multi-period model and in each period the solvency constraints will be updated. Moreover, the model has the inactive state including some uninsured population. Similar results on the existence of premium equilibrium and sensitivity analysis for this model are presented and illustrated by numerical results.