Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance mo...Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance model. By introducing a set of constraint constants to measure uncertainty degree of the estimated expected return,it built the max-min model of multi-prior portfolio,and utilized the Lagrange method to obtain the closed-form solution of the model,which was compared with the mean-variance model and the minimum-variance model; then,an empirical study was done based on the monthly returns over the period June 2011 to May 2014 of eight kinds of stocks in Shanghai Exchange 50 Index. Results showed,the weight of multi-prior portfolio was a weighted average of the weight of mean-variance portfolio and that of minimumvariance portfolio; the steady of multi-prior portfolio was strengthened compared with the mean-variance portfolio; the performance of multi-prior portfolio was greater than that of minimum-variance portfolio. The study demonstrates that the investor can improve the steady of multi-prior portfolio as well as its performance for some appropriate constraint constants.展开更多
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
In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain wit...In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.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
In reality,when facing a multi-period asset-liability portfolio selection problem,the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level.Thus,in this paper,we propose...In reality,when facing a multi-period asset-liability portfolio selection problem,the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level.Thus,in this paper,we propose a state-dependent risk aversion model for the investor,in which risk aversion is a linear function of current wealth level and current liability level.Due to the time inconsistency of the resulting multi-period asset-liability mean-variance model,we investigate its time-consistent portfolio policy by solving a nested mean-variance game formulation.We derive the analytical time-consistent portfolio policy,which takes a linear form of current wealth level and current liability level.We also analyze the influence of the risk aversion coefficients on the time-consistent portfolio policy and the investment performance via a numerical example.展开更多
This study aims to reduce the statistical uncertainty of the correlation coefficient matrix in the mean-variance model of Markowitz.A filtering algorithm based on minimum spanning tree(MST)is proposed.Daily data of th...This study aims to reduce the statistical uncertainty of the correlation coefficient matrix in the mean-variance model of Markowitz.A filtering algorithm based on minimum spanning tree(MST)is proposed.Daily data of the 30 stocks of the Hang Seng Index(HSI)and Dow Jones Index(DJI)from 2004 to 2009 are selected as the base dataset.The proposed algorithm is compared with the Markowitz method in terms of risk,reliability,and effective size of the portfolio.Results show that(1)although the predicted risk of portfolio built with the MST is slightly higher than that of Markowitz,the realized risk of MST filtering algorithm is much smaller;and(2)the reliability and the effective size of filtering algorithm based on MST is apparently better than that of the Markowitz portfolio.Therefore,conclusion is that filtering algorithm based on MST improves the mean-variance model of Markowitz.展开更多
Optimization problem of cardinality constrained mean-variance(CCMV)model for sparse portfolio selection is considered.To overcome the difficulties caused by cardinality constraint,an exact penalty approach is employed...Optimization problem of cardinality constrained mean-variance(CCMV)model for sparse portfolio selection is considered.To overcome the difficulties caused by cardinality constraint,an exact penalty approach is employed,then CCMV problem is transferred into a difference-of-convex-functions(DC)problem.By exploiting the DC structure of the gained problem and the superlinear convergence of semismooth Newton(ssN)method,an inexact proximal DC algorithm with sieving strategy based on a majorized ssN method(siPDCA-mssN)is proposed.For solving the inner problems of siPDCA-mssN from dual,the second-order information is wisely incorporated and an efficient mssN method is employed.The global convergence of the sequence generated by siPDCA-mssN is proved.To solve large-scale CCMV problem,a decomposed siPDCA-mssN(DsiPDCA-mssN)is introduced.To demonstrate the efficiency of proposed algorithms,siPDCA-mssN and DsiPDCA-mssN are compared with the penalty proximal alternating linearized minimization method and the CPLEX(12.9)solver by performing numerical experiments on realword market data and large-scale simulated data.The numerical results demonstrate that siPDCA-mssN and DsiPDCA-mssN outperform the other methods from computation time and optimal value.The out-of-sample experiments results display that the solutions of CCMV model are better than those of other portfolio selection models in terms of Sharp ratio and sparsity.展开更多
基金National Natural Science Foundations of China(Nos.71271003,71171003)Programming Fund Project of the Humanities and Social Sciences Research of the Ministry of Education of China(No.12YJA790041)
文摘Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance model. By introducing a set of constraint constants to measure uncertainty degree of the estimated expected return,it built the max-min model of multi-prior portfolio,and utilized the Lagrange method to obtain the closed-form solution of the model,which was compared with the mean-variance model and the minimum-variance model; then,an empirical study was done based on the monthly returns over the period June 2011 to May 2014 of eight kinds of stocks in Shanghai Exchange 50 Index. Results showed,the weight of multi-prior portfolio was a weighted average of the weight of mean-variance portfolio and that of minimumvariance portfolio; the steady of multi-prior portfolio was strengthened compared with the mean-variance portfolio; the performance of multi-prior portfolio was greater than that of minimum-variance portfolio. The study demonstrates that the investor can improve the steady of multi-prior portfolio as well as its performance for some appropriate constraint constants.
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In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.
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This research was supported by the National Natural Science Foundation of China(Nos.71601107,71671106 and 71201094)Shanghai Pujiang Program(No.15PJC051)+1 种基金the State Key Program in the Major Research Plan of National Natural Science Foundation of China(No.91546202)Program for Innovative Research Team of Shanghai University of Finance and Economics.
文摘In reality,when facing a multi-period asset-liability portfolio selection problem,the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level.Thus,in this paper,we propose a state-dependent risk aversion model for the investor,in which risk aversion is a linear function of current wealth level and current liability level.Due to the time inconsistency of the resulting multi-period asset-liability mean-variance model,we investigate its time-consistent portfolio policy by solving a nested mean-variance game formulation.We derive the analytical time-consistent portfolio policy,which takes a linear form of current wealth level and current liability level.We also analyze the influence of the risk aversion coefficients on the time-consistent portfolio policy and the investment performance via a numerical example.
基金supported by the funds project under the Ministry of Education of the PRC for young people who are devoted to the researches of humanities and social sciences under Grant No.09YJC790025
文摘This study aims to reduce the statistical uncertainty of the correlation coefficient matrix in the mean-variance model of Markowitz.A filtering algorithm based on minimum spanning tree(MST)is proposed.Daily data of the 30 stocks of the Hang Seng Index(HSI)and Dow Jones Index(DJI)from 2004 to 2009 are selected as the base dataset.The proposed algorithm is compared with the Markowitz method in terms of risk,reliability,and effective size of the portfolio.Results show that(1)although the predicted risk of portfolio built with the MST is slightly higher than that of Markowitz,the realized risk of MST filtering algorithm is much smaller;and(2)the reliability and the effective size of filtering algorithm based on MST is apparently better than that of the Markowitz portfolio.Therefore,conclusion is that filtering algorithm based on MST improves the mean-variance model of Markowitz.
基金supported by the National Natural Science Foundation of China(Grant No.11971092)supported by the Fundamental Research Funds for the Central Universities(Grant No.DUT20RC(3)079)。
文摘Optimization problem of cardinality constrained mean-variance(CCMV)model for sparse portfolio selection is considered.To overcome the difficulties caused by cardinality constraint,an exact penalty approach is employed,then CCMV problem is transferred into a difference-of-convex-functions(DC)problem.By exploiting the DC structure of the gained problem and the superlinear convergence of semismooth Newton(ssN)method,an inexact proximal DC algorithm with sieving strategy based on a majorized ssN method(siPDCA-mssN)is proposed.For solving the inner problems of siPDCA-mssN from dual,the second-order information is wisely incorporated and an efficient mssN method is employed.The global convergence of the sequence generated by siPDCA-mssN is proved.To solve large-scale CCMV problem,a decomposed siPDCA-mssN(DsiPDCA-mssN)is introduced.To demonstrate the efficiency of proposed algorithms,siPDCA-mssN and DsiPDCA-mssN are compared with the penalty proximal alternating linearized minimization method and the CPLEX(12.9)solver by performing numerical experiments on realword market data and large-scale simulated data.The numerical results demonstrate that siPDCA-mssN and DsiPDCA-mssN outperform the other methods from computation time and optimal value.The out-of-sample experiments results display that the solutions of CCMV model are better than those of other portfolio selection models in terms of Sharp ratio and sparsity.
