STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

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.

Research on Efficient Frontier of Portfolios with Transaction Cost

This paper is concerned with a study on the efficient frontier characters of portfolio with transaction cost. The conclusion is drawn that all portfolios are of positive correlation on the efficient frontier with transaction cost; the sufficient condition for the derivable efficient frontier has also been achieved. Meanwhile, in comparison with the position of the efficient frontier without transaction cost in the plane (σ 2,R), the conclusion has been made that the efficient frontiers with transaction cost drift and its opening shrinks correspondingly. With this study, the content of the efficient frontier is further enriched. It’s very constructive and important for the practical portfolio investment strategy.

Spatial-temporal Divergence Characteristics and Driving Factors of Green Economic Efficiency in the Yangtze River Economic Belt of China

The spatial and temporal variation of green economic efficiency and its driving factors are of great significance for the con-struction of high-efficiency and low-consumption green development model and sustainable socio-economic development.The research focused on the Yangtze River Economic Belt(YREB)and employed the miniumum distance to strong efficient frontier DEA(MinDs)model to measure the green economic efficiency of the municipalities in the region between 2008 and 2020.Then,the spatial autocorrel-ation model was used to analyze the evolution characteristics of its spatial pattern.Finally,Geodetector was applied to reveal the drivers and their interactions on green economic efficiency.It is found that:1)the overall green economic efficiency of the YREB from 2008 to 2020 shows a W-shaped fluctuating upward trend,green economic efficiency is greater in the downstream and smallest in the upstream;2)the spatial distribution of green economic efficiency shows clustering characteristics,with multi-core clustering based on‘city clusters-central cities'becoming more obvious over time;the High-High agglomeration type is mainly clustered in Jiangsu and Zheji-ang,while the Low-Low agglomeration type is clustered in the western Sichuan Plateau area and southwestern Yunnan;3)from input-output factors,whether it is the YREB as a whole or the upper,middle and lower reaches regions,the economic development level,labor input,and capital investment are the leading factors in the spatial-temporal evolution of green economic efficiency,with the com-prehensive influence of economic development level and pollution index being the most important interactive driving factor;4)from so-cio-economic factors,information technology drivers such as government intervention,transportation accessibility,information infra-structure,and Internet penetration are always high impact influencers and dominant interaction factors for green economic efficiency in the YREB and the three major regions in the upper,middle and lower reaches.Accordingly,the article puts forward relevant policy re-commendations in terms of formulating differentiated green transformation strategies,strengthening network leadership and informa-tion technology construction and coordinating multi-factor integrated development,which could provide useful reference for promoting synergistic green economic efficiency in the YREB.

The Identifying of the Efficient Market Portfolio

The capital-asset pricing model （CAPM） discovered by Sharp （1964）, Lintner （1965） and Mossin （1966） is a general equilibrium model. It not only allows improved understanding of market behavior, but also provides practical benefits. At the same time, it also provides a practical mechanism for evaluating performance in a risk-adjusted mode. This model thus provides the initial basis for the practical implementation of the many aspects of portfolio analysis. However, Richard Roll （1977） has directed some biting criticism at the tests in affirming the CAPM. This criticism is aimed at one of the critical notions-the identifying of the efficient market portfolio. This paper solves the highly difficult problem by a geometrical way. It first denotes the efficient frontier of Markowitz model with the weights vector of portfolio. Then, it denotes the capital market line （CML） with the weights vector too. By the definition of the CML, the efficient market portfolio thus can be identified.

A novel hybrid algorithm based on a harmony search and artificial bee colony for solving a portfolio optimization problem using a mean-semi variance approach

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.

MARKOV-MODULATED MEAN-VARIANCE PROBLEM FOR AN INSURER

In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.

The Extent of Voluntary Information in the Annual Report and the Share Price Volatility： Application of DEA and SFA on the French Market

In the current paper, the authors investigate empirically the relationship between the share price volatility and the amount of voluntary information disclosed in the corporate annual report. The authors use the data envelopment analysis （DEA） and the stochastic frontier analysis （SFA） models on a sample of 50 listed French firms belonging to the Soci6t6s des Bourses Fran^aises （SBF250） index from 2004 to 2008. The authors focus on the extent of voluntary disclosure in the annual reports that have been measure by using a composite disclosure index. Then, the authors study the relevance of disclosure policies through the ability of the voluntary disclosure level to effectively reduce the share price volatility. The findings of DEA and SFA provide, in average, highly efficient scores of the sample, reveal the several dispositions taken by the French Exchange Market authorities and the initiative of French firms to improve the market stability. In addition, the findings highlight, in average, stability of the firms＇ efficiency scores over the studied period. The authors explain these findings by the stability of corporate disclosure policy as suggested in previous literature （e.g., Botosan, 1997）. However, there are some differences between the findings of SFA and DEA models.

Technical efficiency and its determinants of the various cropping systems in the purple-soiled,hilly region of southwestern China

This study examines the technical efficiency(TE) differences among typical cropping systems of smallholder farmers in the purple-soiled hilly region of southwestern China.Household-,plot-,and crop-level data and community surveys were conducted to explore TE levels and determinants of typical cropping systems by using a translog stochastic frontier production function.Results indicate significant difference in TE and its determinants among cropping systems.The mean TEs of the rice cropping system(R),the rice-rape cropping system(RR),the rice-rape-potato cropping system(RRP),and the oil cropping system(O) are0.86,0.90,0.84,and 0.85,respectively,which are over 1.17 times higher than those of the maize-sweet potato-other crop cropping system(MSO) and the maize-sweet potato-wheat cropping system(MSW) at0.78 and 0.69,respectively.Moreover,Technical inefficiency(TIE) of different cropping systems is significantly affected by characteristics of the household as well as plot.However,the impact of land quality,mechanical cultivation conditions,crop structure,farming system,farm radius,household type,cultivated land area per capita,and annual household income per capitalon TIE vary by cropping system.Additionally,output elasticity of land,labor,and capital,as a group,is greater than the one of agricultural machinery and irrigation.Finally,when household-owned effective agricultural labor is at full farming capacity,optimal plot sizes for the R,RR,RRP,MSO,MSW,and 0 cropping systems are 1.12hm^2,0.35 hm^2,0.25 hm^2,2.82 hm^2,1.87 hm^2,and 1.17hm^2,respectively.

Research on the Portfolio with Transaction Cost and Inflation

This paper analyzes the portfolio with inflation and transaction cost by broadening mean-variance model assumption. Based on the comparison between efficient frontier with and without transaction cost and inflation, the conclusion is drawn that the new efficient frontier is revolving and the new investment strategy changes. Furthermore, we provide a numerical example based on real world data.

A Value-at-Risk Based Approach for PMU Placement in Distribution Systems

With the application of phasor measurement units(PMU)in the distribution system,it is expected that the performance of the distribution system state estimation can be improved obviously with the PMU measurements into consideration.How to appropriately place the PMUs in the distribution is therefore become an important issue due to the economical consideration.According to the concept of efficient frontier,a value-at-risk based approach is proposed to make optimal placement of PMU taking account of the uncertainty of measure errors,statistical characteristics of the pseudo measurements,and reliability of the measurement instrument.The reasonability and feasibility of the proposed model is illustrated with 12-node system and IEEE-33 node system.Simulation results indicated that uncertainties of measurement error and instrument fault result in more PMU to be installed,and measurement uncertainty is the main affect factor unless the fault rate of PMU is quite high.

Portfolio Selection Using Double GAs Searching for Cardinality and Integer Multiplied Optimal Weights

This paper studied cardinality constrained portfolio with integer weight.We suggested two optimization models and used two genetic algorithms to solve them.In this paper,after finding well matching stocks,according to investor’s target by using first genetic algorithm,we gave optimal integer weight of portfolio with well matching stocks by using second genetic algorithm.Through numerical comparisons with other feasible portfolios,we verified advantages of designed portfolio with two genetic algorithms.For a numerical comparison,we used a prepared data consisted of 18 stocks listed in S&P 500 and numerical example strongly supported the designed portfolio in this paper.Also,we made all comparisons visible through all feasible efficient frontiers.

A review on trade-off analysis of ecosystem services for sustainable land-use management

Ecosystem services are substantial elements for human society. The central challenge to meet the human needs from ecosystems while sustain the Earth's life support systems makes it urgent to enhance efficient natural resource management for sustainable ecological and socioeconomic development. Trade-off analysis of ecosystem services can help to identify optimal decision points to balance the costs and benefits of the diverse human uses of ecosystems. In this sense, the aim of this paper is to provide key insights into ecosystem services trade-off analysis at different scales from a land use perspective, by comprehensively reviewing the trade-offs analysis tools and approaches that addressed in ecology, economics and other fields. The review will significantly contribute to future research on trade-off analysis to avoid inferior management options and offer a win-win solution based on comprehensive and efficient planning for interacting multiple ecosystem services.

MIXED HEDGING UNDER ADDITIVE MARKET PRICE INFORMATION

Assume that there is additional market information in the financial market, which is represented by n given T-contingent claims. The special claims with observed prices at time 0 can only be traded at time 0. Hence, investment opportunities increase. By means of the techniques developed by Gourierout et al. （1998）, the mixed hedging problem is considered, especially, the price of contingent claim and the optimal hedging strategy are obtained. An explicit description of the mean-variance efficient solution is given after arguing mean-variance efficient frontier problem.

Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework

This paper studies a dynamic mean-variance portfolio selection problem with random liability in the affine interest rate environment, where the financial market consists of three assets: one risk-free asset, one risky asset and one zero-coupon bond. Assume that short rate is driven by affine interest rate model and liability process is described by the drifted Brownian motion, in addition, stock price dynamics is affected by interest rate dynamics. The investors expect to look for an optimal strategy to minimize the variance of the terminal surplus for a given expected terminal surplus. The efficient strategy and the efficient frontier are explicitly obtained by applying dynamic programming principle and Lagrange duality theorem. A numerical example is given to illustrate our results and some economic implications are analyzed.

Portfolio Optimization with Uncertain Exit Time in Infinite-Time Horizon

In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.

Mean-variance Portfolio Selections in Continuous-time Model with Stochastic Interest Rate Process

Under the continuous time （d＋1） assets market model with finite time horizon T, and the condition that all coefficients in model are stochastic processes, the decision of investment portfolio selection had been studied. By using K.Itǒ formuia and backward stochastic differential equation＇s theory, on the relation of investment portfolio processes, fortune processes, the backward stochastic differential equation model for stochastic control problem had been established, the relation between the prime fortune process and the end- all fortune process had been proposed, the existence and uniqueness of investment portfolio had been proved, and the formula for investment portfolio had been arrived. On the setting of mean-variance portfolio selection, we obtained the formula of optimal efficient investment portfolio. Furthermore, the mean-variance efficient frontier is too obtained explicitly in the form of parameter.