In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial ...In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities.展开更多
Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk...Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.展开更多
In this paper, based on existing results, decision making about portfolio investment schemes is discussed, ordering method of fuzzy numbers of interval value is shown, corresponding auxiliary models are established an...In this paper, based on existing results, decision making about portfolio investment schemes is discussed, ordering method of fuzzy numbers of interval value is shown, corresponding auxiliary models are established and solutions are provided with theories of fuzzy mathematics, optimization theory and numerical calculation, etc. Then it applies software programming to solve the portfolio investment situation between investors in savings and four securities according to the established models. The result shows that investors can choose the risk coefficient that they can bear to reach the maximum value of expected returns. The greater the risk coefficient, the greater the income, the smaller the risk coefficient and the smaller the income. Investors can determine their own portfolio strategy according to their own conditions in order to meet their own interests.展开更多
The theory of investment portfolio is a very important theory in the modern economical system. Based on the feature of the theory, the paper sets up new various kinds of models of investment portfolio, namely grey opt...The theory of investment portfolio is a very important theory in the modern economical system. Based on the feature of the theory, the paper sets up new various kinds of models of investment portfolio, namely grey optimization models. These models are more practical and objective to existing problems.展开更多
In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper ...In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.展开更多
A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is dev...A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is developed. The stochastic 2 D FMM Ⅱ with multiplicative noise can be reduced to a 1 D model, and the proposed optimal filtering algorithm for the stochastic 2 D FMM Ⅱ with multiplicative noise is obtained by using the state estimation theory of 1 D systems. An example is given to illustrate the validity of this algorithm.展开更多
To solve the problem of investment portfolio with single goal of maximal NPV, a 0- 1 programming model was proposed and proved effective; and to solve that concerning more elements of a project such as risk level and ...To solve the problem of investment portfolio with single goal of maximal NPV, a 0- 1 programming model was proposed and proved effective; and to solve that concerning more elements of a project such as risk level and social benefit, a goal programming model is then introduced. The latter is a linear programming model adopting slack variable called deviation variable to turn inequation constraint into equation constraint, introducing a priority factor to denote different importance of the goals. A case study has demonstrated that this goal programming model can give different results according to different priority requirement of each objective.展开更多
The article gives readers the main regulations of elaboration of capital actives evaluating model(CAPM)theory,topics of its practical usage,common ways of definition of investments(securities)optimal portfolio and on ...The article gives readers the main regulations of elaboration of capital actives evaluating model(CAPM)theory,topics of its practical usage,common ways of definition of investments(securities)optimal portfolio and on the basis of CAPM theory it is discussed evaluating methods of investing business,and it is highlighted two criteria of portfolio chosen by an investor—profit and risk.Besides,it is discussed modern modification of the mentioned model on the point of time horizon,a problem of time factor measurement while evaluating risk and profit,also evaluation of investing effectivity by using sharp coefficient.The work presents and evaluates possible income of securities and possibilities of risks in a modern way,which is characteristic only for CAPM model and it is considered to be its positive side.展开更多
The purpose of the article is to formulate, under the ∞ risk measure, a model of portfolio selection with transaction costs and then investigate the optimal strategy within the proposed. The characterization of a opt...The purpose of the article is to formulate, under the ∞ risk measure, a model of portfolio selection with transaction costs and then investigate the optimal strategy within the proposed. The characterization of a optimal strategy and the efficient algorithm for finding the optimal strategy are given.展开更多
In the real-world environments,different individuals have different risk preferences.This paper investigates the optimal portfolio and consumption rule with a Cox–Ingersoll–Ross(CIR)model in a more general utility f...In the real-world environments,different individuals have different risk preferences.This paper investigates the optimal portfolio and consumption rule with a Cox–Ingersoll–Ross(CIR)model in a more general utility framework.After consumption,an individual invests his wealth into the financial market with one risk-free asset and multiple risky assets,where the short-term rate is driven by the CIR model and stock price dynamics are simultaneously influenced by random sources from both stochastic interest rate and stock market itself.The individual hopes to optimize their portfolios and consumption rules to maximize expected utility of terminal wealth and intermediate consumption.Risk preference of individual is assumed to satisfy hyperbolic absolute risk aversion(HARA)utility,which contains power utility,logarithm utility,and exponential utility as special cases.By using the principle of stochastic optimality and Legendre transform-dual theory,the explicit expressions of the optimal portfolio and consumption rule are obtained.The sensitivity of the optimal strategies to main parameters is analysed by a numerical example.In addition,economic implications are also presented.Our research results show that Legendre transform-dual theory is an effective methodology in dealing with the portfolio selection problems with HARA utility and interest rate risk can be completely hedged by constructing specific portfolios.展开更多
In this paper, a convex programming model for portfolio select with trans- action costs was present, we proved the existence condition of optimal solution, and gave a simple example to the optimal solution.
基金Project supported by the National Natural Science Foundation of China （Grant Nos.70518001. 70671064）
文摘In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities.
文摘Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.
文摘In this paper, based on existing results, decision making about portfolio investment schemes is discussed, ordering method of fuzzy numbers of interval value is shown, corresponding auxiliary models are established and solutions are provided with theories of fuzzy mathematics, optimization theory and numerical calculation, etc. Then it applies software programming to solve the portfolio investment situation between investors in savings and four securities according to the established models. The result shows that investors can choose the risk coefficient that they can bear to reach the maximum value of expected returns. The greater the risk coefficient, the greater the income, the smaller the risk coefficient and the smaller the income. Investors can determine their own portfolio strategy according to their own conditions in order to meet their own interests.
基金This project is supported by National Natural Science Foundation of China (No. 19871009)
文摘The theory of investment portfolio is a very important theory in the modern economical system. Based on the feature of the theory, the paper sets up new various kinds of models of investment portfolio, namely grey optimization models. These models are more practical and objective to existing problems.
基金Supported by the NNSF of China (10571141) the Key Project of the NNSF of China (70531030).
文摘In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.
基金supported by NSFS Project for Tianyuan Mathematical Fund(No.A0324676)the Science&Technology Research Key Projects of the Ministry of Education of China(No.02131).
文摘A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is developed. The stochastic 2 D FMM Ⅱ with multiplicative noise can be reduced to a 1 D model, and the proposed optimal filtering algorithm for the stochastic 2 D FMM Ⅱ with multiplicative noise is obtained by using the state estimation theory of 1 D systems. An example is given to illustrate the validity of this algorithm.
基金Funded by the Foundation of Science Committee of Chongqing (No.2000- 6071)
文摘To solve the problem of investment portfolio with single goal of maximal NPV, a 0- 1 programming model was proposed and proved effective; and to solve that concerning more elements of a project such as risk level and social benefit, a goal programming model is then introduced. The latter is a linear programming model adopting slack variable called deviation variable to turn inequation constraint into equation constraint, introducing a priority factor to denote different importance of the goals. A case study has demonstrated that this goal programming model can give different results according to different priority requirement of each objective.
文摘The article gives readers the main regulations of elaboration of capital actives evaluating model(CAPM)theory,topics of its practical usage,common ways of definition of investments(securities)optimal portfolio and on the basis of CAPM theory it is discussed evaluating methods of investing business,and it is highlighted two criteria of portfolio chosen by an investor—profit and risk.Besides,it is discussed modern modification of the mentioned model on the point of time horizon,a problem of time factor measurement while evaluating risk and profit,also evaluation of investing effectivity by using sharp coefficient.The work presents and evaluates possible income of securities and possibilities of risks in a modern way,which is characteristic only for CAPM model and it is considered to be its positive side.
基金Supported by the National Natural Sciences Foundation of China.
文摘The purpose of the article is to formulate, under the ∞ risk measure, a model of portfolio selection with transaction costs and then investigate the optimal strategy within the proposed. The characterization of a optimal strategy and the efficient algorithm for finding the optimal strategy are given.
基金This research is supported by National Natural Science Foundation of China(No.71671122)China Postdoctoral Science Foundation Funded Project(Nos.2014M560185 and 2016T90203)+1 种基金Humanities and Social Science Research Fund of Ministry of Education of China(Nos.11YJC790006 and 16YJA790004)Tianjin Natural Science Foundation of China(No.15JCQNJC04000).
文摘In the real-world environments,different individuals have different risk preferences.This paper investigates the optimal portfolio and consumption rule with a Cox–Ingersoll–Ross(CIR)model in a more general utility framework.After consumption,an individual invests his wealth into the financial market with one risk-free asset and multiple risky assets,where the short-term rate is driven by the CIR model and stock price dynamics are simultaneously influenced by random sources from both stochastic interest rate and stock market itself.The individual hopes to optimize their portfolios and consumption rules to maximize expected utility of terminal wealth and intermediate consumption.Risk preference of individual is assumed to satisfy hyperbolic absolute risk aversion(HARA)utility,which contains power utility,logarithm utility,and exponential utility as special cases.By using the principle of stochastic optimality and Legendre transform-dual theory,the explicit expressions of the optimal portfolio and consumption rule are obtained.The sensitivity of the optimal strategies to main parameters is analysed by a numerical example.In addition,economic implications are also presented.Our research results show that Legendre transform-dual theory is an effective methodology in dealing with the portfolio selection problems with HARA utility and interest rate risk can be completely hedged by constructing specific portfolios.
文摘In this paper, a convex programming model for portfolio select with trans- action costs was present, we proved the existence condition of optimal solution, and gave a simple example to the optimal solution.
