In this paper, we focus on a constant elasticity of variance （CEV） modeland want to find its optimal strategies for a mean-variance problem under two constrainedcontrols： reinsurance/new business and investment （n...In this paper, we focus on a constant elasticity of variance （CEV） modeland want to find its optimal strategies for a mean-variance problem under two constrainedcontrols： reinsurance/new business and investment （no-shorting）. First, aLagrange multiplier is introduced to simplify the mean-variance problem and thecorresponding Hamilton-Jacobi-Bellman （HJB） equation is established. Via a powertransformation technique and variable change method, the optimal strategies withthe Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem,the optimal strategies and optimal value for the original problem （i.e., the efficientstrategies and efficient frontier） are derived explicitly.展开更多
The article introduces proportional reinsurance contracts under the mean-variance criterion,studying the time-consistence investment portfolio problem considering the interests of both insurance companies and reinsura...The article introduces proportional reinsurance contracts under the mean-variance criterion,studying the time-consistence investment portfolio problem considering the interests of both insurance companies and reinsurance companies.The insurance claims process follows a jump-diffusion model,assuming that the risk asset prices of insurance companies and reinsurance companies follow CEV models different from each other.In the framework of game theory,the time-consistent equilibrium reinsurance strategy is obtained by solving the extended HJB equation analytically.Finally,numerical examples are used to illustrate the impact of model parameters on equilibrium strategies and provide economic explanations.The results indicate that the decision weights of insurance companies and reinsurance companies do have a significant impact on both the reinsurance ratio and the equilibrium reinsurance strategy.展开更多
Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan...Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model.We examine the point symmetries of the Hamilton-Jacobi-Bellman(HJB)equation associated with the portfolio optimization problem.The symmetries compatible with the terminal condition enable us to transform the(2+1)-dimensional HJB equation into a(1+1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations.Finally,the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained.The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.展开更多
In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows ...In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.展开更多
Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcom...Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.展开更多
Body mass index(BMI)and breast cancer biomarkers(BCBs)such as resistin,leptin adiponectin,monocyte chemoattractant protein-1(MCP-1)and homeostasis model assessment of insulin resistance(HOMA-IR)are highly associated w...Body mass index(BMI)and breast cancer biomarkers(BCBs)such as resistin,leptin adiponectin,monocyte chemoattractant protein-1(MCP-1)and homeostasis model assessment of insulin resistance(HOMA-IR)are highly associated with each other.The report has focused the inter-relationship between BMI and BCBs based on probabilistic modeling.It has been shown that mean BMI is directly associated with leptin(P<0.0001)and MCP-1(P=0.0002),while it is inversely associated with adiponectin(P=0.0003),HOMA-IR(P<0.0001),and it is higher for healthy women(P=0.0116)than breast cancer women.In addition,variance of BMI is inversely associated with resistin(P=0.1450).On the other hand,mean MCP-1 is directly associated with BMI(P<0.0001).Mean resistin is directly associated with the interaction effect of BMI and leptin(BMI^*Leptin)(P=0.0415),while its variance is directly associated with BMI(P=0.0942),and it is inversely associated with BMI*Adiponectin(P=0.1518).Leptin is directly associated with BMI(P<0.0001).Also adiponectin is inversely associated with BMI(P<0.0001),BMI*Leptin(P=0.1729),while it is directly associated with Age^*BMI(P=0.0017)and BMI^*Resistin(P=0.0615).It can be concluded that BMI and BCBs are strongly associated with each other.Care should be taken on BMI for breast cancer women.展开更多
Although genome-wide association studies are widely used to mine genes for quantitative traits,the effects to be estimated are confounded,and the methodologies for detecting interactions are imperfect.To address these...Although genome-wide association studies are widely used to mine genes for quantitative traits,the effects to be estimated are confounded,and the methodologies for detecting interactions are imperfect.To address these issues,the mixed model proposed here first estimates the genotypic effects for AA,Aa,and aa,and the genotypic polygenic background replaces additive and dominance polygenic backgrounds.Then,the estimated genotypic effects are partitioned into additive and dominance effects using a one-way analysis of variance model.This strategy was further expanded to cover QTN-by-environment interactions(QEIs)and QTN-by-QTN interactions(QQIs)using the same mixed-model framework.Thus,a three-variance-component mixed model was integrated with our multi-locus random-SNP-effect mixed linear model(mrMLM)method to establish a new methodological framework,3VmrMLM,that detects all types of loci and estimates their effects.In Monte Carlo studies,3VmrMLM correctly detected all types of loci and almost unbiasedly estimated their effects,with high powers and accuracies and a low false positive rate.In re-analyses of 10 traits in 1439 rice hybrids,detection of 269 known genes,45 known gene-by-environment interactions,and 20 known gene-by-gene interactions strongly validated 3VmrMLM.Further analyses of known genes showed more small(67.49%),minor-allele-frequency(35.52%),and pleiotropic(30.54%)genes,with higher repeatability across datasets(54.36%)and more dominance loci.In addition,a heteroscedasticity mixed model in multiple environments and dimension reduction methods in quite a number of environments were developed to detect QEIs,and variable selection under a polygenic background was proposed for QQI detection.This study provides a new approach for revealing the genetic architecture of quantitative traits.展开更多
The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework.The paper is distinguished from other literature by taking into account the interests of both an...The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework.The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer jointly.The claim process of the insurer is governed by a Brownian motion with a drift.A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle.Both the insurer and the reinsurer are assumed to invest in a risky asset,which is distinct for each other and driven by a constant elasticity of variance model.The optimal decision is formulated on a weighted sum of the insurer’s and the reinsurer’s surplus processes.Upon a verification theorem,which is established with a formal proof for a more general problem,explicit solutions are obtained for the proposed investment-reinsurance model.Moreover,numerous mathematical analysis and numerical examples are provided to demonstrate those derived results as well as the economic implications behind.展开更多
This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of...This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance(CEV) model.Compared with the geometric Brownian motion model,the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile.The authors assume that the contribution to the pension fund is a constant proportion of the pension member's salary.Meanwhile,the salary is stochastic and its volatility arises from the price process of the risky asset,which makes the proposed model different from most of existing researches and more realistic.In the proposed model,the optimization problem can be decomposed into two sub-problems:Before and after retirement cases.By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman(HJB) systems,the authors derive the time-consistent strategies and the corresponding value functions explicitly.Finally,numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.展开更多
Over the past few years, the Utah Department of Transportation has developed the signal performance metrics （SPMs） system to evaluate the performance of signalized in- tersections dynamically. This system currently ...Over the past few years, the Utah Department of Transportation has developed the signal performance metrics （SPMs） system to evaluate the performance of signalized in- tersections dynamically. This system currently provides data summaries for several per- formance measures, one of them being turning movement counts collected by microwave sensors. As this system became public, there was a need to evaluate the accuracy of the data placed on the SPMs. A large-scale data collection was carried out to meet this need. Vehicles in the Hi-resolution data from microwave sensors were matched with the vehicles by ground-truth volume count data. Matching vehicles from the microwave sensor data and the ground-truth data manually collected required significant effort, A spreadsheet- based data analysis procedure was developed to carry out the task. A mixed model analysis of variance was used to analyze the effects of the factors considered on turning volume count accuracy. The analysis found that approach volume level and number of approach lanes would have significant effect on the accuracy of turning volume counts but the location of the sensors did not significantly affect the accuracy of turning volume counts. In addition, it was found that the location of lanes in relation to the sensor did not significantly affect the accuracy of lane-by-lane volume counts. This indicated that accu- racy analysis could be performed by using total approach volumes without comparing specific turning counts, that is, left-turn, through and right-turn movements. In general, the accuracy of approach volume counts collected by microwave sensors were within the margin of error that traffic engineers could accept. The procedure taken to perform the analysis and a summary of accuracy of volume counts for the factor combinations considered are presented in this paper.展开更多
基金The NSF(11201111) of ChinaHebei Province Colleges and Universities Science,and Technology Research Project(ZD20131017)
文摘In this paper, we focus on a constant elasticity of variance （CEV） modeland want to find its optimal strategies for a mean-variance problem under two constrainedcontrols： reinsurance/new business and investment （no-shorting）. First, aLagrange multiplier is introduced to simplify the mean-variance problem and thecorresponding Hamilton-Jacobi-Bellman （HJB） equation is established. Via a powertransformation technique and variable change method, the optimal strategies withthe Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem,the optimal strategies and optimal value for the original problem （i.e., the efficientstrategies and efficient frontier） are derived explicitly.
文摘The article introduces proportional reinsurance contracts under the mean-variance criterion,studying the time-consistence investment portfolio problem considering the interests of both insurance companies and reinsurance companies.The insurance claims process follows a jump-diffusion model,assuming that the risk asset prices of insurance companies and reinsurance companies follow CEV models different from each other.In the framework of game theory,the time-consistent equilibrium reinsurance strategy is obtained by solving the extended HJB equation analytically.Finally,numerical examples are used to illustrate the impact of model parameters on equilibrium strategies and provide economic explanations.The results indicate that the decision weights of insurance companies and reinsurance companies do have a significant impact on both the reinsurance ratio and the equilibrium reinsurance strategy.
基金supported in part by the 13th Five-Year National Key Research and Development Program of China(Grant No.2016YFCO401407)the National Natural Science Foundation of China(Grant No.72071076)+1 种基金the Beijing NaturalScience Foundation(Grant No.Z200001)the Fundamental Research Funds of the Central Universities(Grant Nos.2019MS050,2020MS043).
文摘Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model.We examine the point symmetries of the Hamilton-Jacobi-Bellman(HJB)equation associated with the portfolio optimization problem.The symmetries compatible with the terminal condition enable us to transform the(2+1)-dimensional HJB equation into a(1+1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations.Finally,the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained.The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.
基金Supported by the National Natural Science Foundation of Tianjin (07JCYBJC05200)the Young Scholar Program of Tianjin University of Finance and Economics (TJYQ201201)
文摘In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.
基金Supported by the National Natural Science Foundation of China(11261025,11201412)the Natural Science Foundation of Yunnan Province(2011FB016)the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.
文摘Body mass index(BMI)and breast cancer biomarkers(BCBs)such as resistin,leptin adiponectin,monocyte chemoattractant protein-1(MCP-1)and homeostasis model assessment of insulin resistance(HOMA-IR)are highly associated with each other.The report has focused the inter-relationship between BMI and BCBs based on probabilistic modeling.It has been shown that mean BMI is directly associated with leptin(P<0.0001)and MCP-1(P=0.0002),while it is inversely associated with adiponectin(P=0.0003),HOMA-IR(P<0.0001),and it is higher for healthy women(P=0.0116)than breast cancer women.In addition,variance of BMI is inversely associated with resistin(P=0.1450).On the other hand,mean MCP-1 is directly associated with BMI(P<0.0001).Mean resistin is directly associated with the interaction effect of BMI and leptin(BMI^*Leptin)(P=0.0415),while its variance is directly associated with BMI(P=0.0942),and it is inversely associated with BMI*Adiponectin(P=0.1518).Leptin is directly associated with BMI(P<0.0001).Also adiponectin is inversely associated with BMI(P<0.0001),BMI*Leptin(P=0.1729),while it is directly associated with Age^*BMI(P=0.0017)and BMI^*Resistin(P=0.0615).It can be concluded that BMI and BCBs are strongly associated with each other.Care should be taken on BMI for breast cancer women.
基金supported by the National Natural Science Foundation of China(32070557 and 31871242)the Fundamental Research Funds for the Central Universities(2662020ZKPY017)+1 种基金the Huazhong Agricultural University Scientific&Technological Self-Innovation Foundation(2014RC020)the State Key Laboratory of Cotton Biology Open Fund(CB2021B01).
文摘Although genome-wide association studies are widely used to mine genes for quantitative traits,the effects to be estimated are confounded,and the methodologies for detecting interactions are imperfect.To address these issues,the mixed model proposed here first estimates the genotypic effects for AA,Aa,and aa,and the genotypic polygenic background replaces additive and dominance polygenic backgrounds.Then,the estimated genotypic effects are partitioned into additive and dominance effects using a one-way analysis of variance model.This strategy was further expanded to cover QTN-by-environment interactions(QEIs)and QTN-by-QTN interactions(QQIs)using the same mixed-model framework.Thus,a three-variance-component mixed model was integrated with our multi-locus random-SNP-effect mixed linear model(mrMLM)method to establish a new methodological framework,3VmrMLM,that detects all types of loci and estimates their effects.In Monte Carlo studies,3VmrMLM correctly detected all types of loci and almost unbiasedly estimated their effects,with high powers and accuracies and a low false positive rate.In re-analyses of 10 traits in 1439 rice hybrids,detection of 269 known genes,45 known gene-by-environment interactions,and 20 known gene-by-gene interactions strongly validated 3VmrMLM.Further analyses of known genes showed more small(67.49%),minor-allele-frequency(35.52%),and pleiotropic(30.54%)genes,with higher repeatability across datasets(54.36%)and more dominance loci.In addition,a heteroscedasticity mixed model in multiple environments and dimension reduction methods in quite a number of environments were developed to detect QEIs,and variable selection under a polygenic background was proposed for QQI detection.This study provides a new approach for revealing the genetic architecture of quantitative traits.
基金supported by National Natural Science Foundation of China (Grant Nos. 11301376, 71201173 and 71571195)China Scholarship Council, the Natural Sciences and Engineering Research Council of Canada (NSERC)+2 种基金Society of Actuaries Centers of Actuarial Excellence Research Grant, Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2015A030306040)Natural Science Foundation of Guangdong Province of China (Grant No. 2014A030310195)for Ying Tung Eduction Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 151081)
文摘The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework.The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer jointly.The claim process of the insurer is governed by a Brownian motion with a drift.A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle.Both the insurer and the reinsurer are assumed to invest in a risky asset,which is distinct for each other and driven by a constant elasticity of variance model.The optimal decision is formulated on a weighted sum of the insurer’s and the reinsurer’s surplus processes.Upon a verification theorem,which is established with a formal proof for a more general problem,explicit solutions are obtained for the proposed investment-reinsurance model.Moreover,numerous mathematical analysis and numerical examples are provided to demonstrate those derived results as well as the economic implications behind.
基金the National Natural Science Foundation of China under Grant Nos.11201335,11301376,and 71573110
文摘This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance(CEV) model.Compared with the geometric Brownian motion model,the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile.The authors assume that the contribution to the pension fund is a constant proportion of the pension member's salary.Meanwhile,the salary is stochastic and its volatility arises from the price process of the risky asset,which makes the proposed model different from most of existing researches and more realistic.In the proposed model,the optimization problem can be decomposed into two sub-problems:Before and after retirement cases.By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman(HJB) systems,the authors derive the time-consistent strategies and the corresponding value functions explicitly.Finally,numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.
文摘Over the past few years, the Utah Department of Transportation has developed the signal performance metrics （SPMs） system to evaluate the performance of signalized in- tersections dynamically. This system currently provides data summaries for several per- formance measures, one of them being turning movement counts collected by microwave sensors. As this system became public, there was a need to evaluate the accuracy of the data placed on the SPMs. A large-scale data collection was carried out to meet this need. Vehicles in the Hi-resolution data from microwave sensors were matched with the vehicles by ground-truth volume count data. Matching vehicles from the microwave sensor data and the ground-truth data manually collected required significant effort, A spreadsheet- based data analysis procedure was developed to carry out the task. A mixed model analysis of variance was used to analyze the effects of the factors considered on turning volume count accuracy. The analysis found that approach volume level and number of approach lanes would have significant effect on the accuracy of turning volume counts but the location of the sensors did not significantly affect the accuracy of turning volume counts. In addition, it was found that the location of lanes in relation to the sensor did not significantly affect the accuracy of lane-by-lane volume counts. This indicated that accu- racy analysis could be performed by using total approach volumes without comparing specific turning counts, that is, left-turn, through and right-turn movements. In general, the accuracy of approach volume counts collected by microwave sensors were within the margin of error that traffic engineers could accept. The procedure taken to perform the analysis and a summary of accuracy of volume counts for the factor combinations considered are presented in this paper.
