Portfolio Choice under the Mean-Variance Model with Parameter Uncertainty

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.

A Mean-variance Problem in the Constant Elasticity of Variance(CEV) Model

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.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

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.

The Time-Consistent Optimal Reinsurance Strategy of Insurance Group under the CEV Model

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.

AN INEXACT PROXIMAL DC ALGORITHM FOR THE LARGE-SCALE CARDINALITY CONSTRAINED MEAN-VARIANCE MODEL IN SPARSE PORTFOLIO SELECTION

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.

Survey on Multi-period Mean-Variance Portfolio Selection Model

Due to the non-separability of the variance term,the dynamic mean-variance(MV)portfolio optimization problem is inherently difficult to solve by dynamic programming.Li and Ng(Math Finance 10(3):387-406,2000)and Zhou and Li(Appl Math Optim 42(1):19-33,2000)develop the pre-committed optimal policy for such a problem using the embedding method.Following this line of research,researchers have extensively studied the MV portfolio selection model through the inclusion of more practical investment constraints,realistic market assumptions and various financial applications.As the principle of optimality no longer holds,the pre-committed policy suffers from the time-inconsistent issue,i.e.,the optimal policy computed at the intermediate time t is not consistent with the optimal policy calculated at any time before time t.The time inconsistency of the dynamic MV model has become an important yet challenging research topic.This paper mainly focuses on the multi-period mean–variance(MMV)portfolio optimization problem,reviews the essential extensions and highlights the critical development of time-consistent policies.

Time-Consistent Portfolio Policy for Asset-Liability Mean-Variance Model with State-Dependent Risk Aversion

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.

MEAN-VARIANCE MODEL BASED ON FILTERS OF MINIMUM SPANNING TREE

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.

The Impact of General Correlation Under Multi-Period Mean-Variance Asset-Liability Portfolio Management

This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of general correlation is considered,i.e.,the random returns of risky assets and the liability are not only statistically correlated to each other but also correlated to themselves in different time periods.Such a model with a general correlation structure extends the classical multiperiod MVAL models with assumption of independent returns.The authors derive the explicit portfolio policy and the MV efficient frontier for this problem.Moreover,a numerical example is presented to illustrate the efficiency of the proposed solution scheme.

Time-consistent investment and reinsurance strategies for insurers under multi-period mean-variance formulation with generalized correlated returns

The existing literature on investment and reinsurance is limited to the study of continuous-time problems,while discrete-time problems are always ignored by re-searchers.In this study,we first discuss a multi-period investment and reinsurance opti-mization problem under the classical mean-variance framework.When the asset returns with a serially correlated structure,the time-consistent investment and reinsurance strategies are acquired via backward induction.In addition,we propose an alternative time-consistent mean-variance optimization model that contrasts with the classical mean-variance model,and the corresponding optimal strategy and value function are also derived.We find that the investment and reinsurance strategies are both independent of the current wealth for the above two optimization problems,which coincides with the conclusion presented in the continuous-time problems.Most importantly,the above in-vestment strategies with serially correlated structures are both conditional mean-based strategies,rather than unconditional ones.Finally,we compare the investment and rein-surance strategies suggested above based on the simulation approach,to shed light on which investment-reinsurance strategies are more suitable for insurers.

ASSET-LIABILITY MANAGEMENT UNDER BENCHMARK AND MEAN-VARIANCE CRITERIA IN A JUMP DIFFUSION MARKET

This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset＇s price is governed by an exponential Levy process, the liability evolves according to a Levy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.

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.

Online risk‑based portfolio allocation on subsets of crypto assets applying a prototype‑based clustering algorithm

Mean-variance portfolio optimization models are sensitive to uncertainty in risk-return estimates,which may result in poor out-of-sample performance.In particular,the estimates may suffer when the number of assets considered is high and the length of the return time series is not sufficiently long.This is precisely the case in the cryptocur-rency market,where there are hundreds of crypto assets that have been traded for a few years.We propose enhancing the mean-variance(MV)model with a pre-selection stage that uses a prototype-based clustering algorithm to reduce the number of crypto assets considered at each investment period.In the pre-selection stage,we run a prototype-based clustering algorithm where the assets are described by variables representing the profit-risk duality.The prototypes of the clustering partition are auto-matically examined and the one that best suits our risk-aversion preference is selected.We then run the MV portfolio optimization with the crypto assets of the selected cluster.The proposed approach is tested for a period of 17 months in the whole cryp-tocurrency market and two selections of the cryptocurrencies with the higher market capitalization(175 and 250 cryptos).We compare the results against three methods applied to the whole market:classic MV,risk parity,and hierarchical risk parity methods.We also compare our results with those from investing in the market index CCI30.The simulation results generally favor our proposal in terms of profit and risk-profit financial indicators.This result reaffirms the convenience of using machine learning methods to guide financial investments in complex and highly-volatile environments such as the cryptocurrency market.

Empirical analysis on risk of security investment

The paper analyzes the theory and application of Markowitz Mean-Variance Model and CAPM model. Firstly, it explains the development process and standpoints of two models and deduces the whole process in detail. Then 30 stocks are choosen from Shangzheng 50 stocks and are testified whether the prices of Shanghai stocks conform to the two models. With the technique of time series and panel data analysis, the research on the stock risk and effective portfolio by ORIGIN and MATLAB software is conducted. The result shows that Shanghai stock market conforms to Markowitz Mean-Variance Model to a certain extent and can give investors reliable suggestion to gain higher return, but there is no positive relation between system risk and profit ratio and CAPM doesn＇t function well in China＇s security market.

A Note on the Mean-Variance Criteria for Discrete Time Financial Markets

It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.

Modeling and Solving a Multi-Period Inventory Fulfilling and Routing Problem for Hazardous Materials

Any potential damage may be severe once an accident occurs involving hazardous materials.It is therefore important to consider the risk factor concerning hazardous material supply chains,in order to make the best inventory routing decisions.This paper addresses the problem of hazardous material multi-period inventory routing with the assumption of a limited production capacity of a given manufacturer.The goal is to achieve the manufacturer's production plan,the retailer's supply schedule and the transportation routes within a fixed period.As the distribution of hazardous materials over a certain period is essentially a multiple travelling salesmen problem,the authors formulate a loadingdependent risk model for multiple-vehicle transportation and present an integer programming model to maximize the supply chain profit.An improved genetic algorithm considering two dimensions of chromosomes that cover the aforementioned period and supply quantity is devised to handle the integer programming model.Numerical experiments carried out demonstrate that using the proposed multiperiod joint decision-making can significantly increase the overall profit of the supply chain as compared to the use of single period decision repeatedly,while effectively reducing its risk.

Regional green finance development and local green innovation:Evidence from a quasi-natural experiment of green bond issuance in China

Based on provincial panel data in China from 2008 to 2019, this research takes the issuance of China's green bond as a quasi-natural experiment to explore whether China's regional green finance development promotes local green innovation by using the multi-period DID model. The results show that the regional green financial development can promote local green innovation, and the rapid growth of the green bond market driven by policy does improve environmental sound technology innovation. The promotion of regional green finance development to local green innovation is related to the funds allocation of green credit,but not to the issuance scale of green bonds, according to further analysis, because China's development pattern can lead to a lack of endogenous market power and low credit resource allocation efficiency. In addition, the issuance of green bonds can effectively promote the allocation of green credit funds, thus enhancing the local green innovation level, but it can't reduce local carbon emissions through promoting green innovation. Therefore, the government should strengthen the green finance implementation assessment mechanism, taking into account the heterogeneity of regions and enterprises, complete the green finance monitoring and disclosure system, and increase the rate of green technology conversion.

An Empirical Analysis on the Stable Return of Resident Funds

This paper mainly studies how investors invest in funds to obtain high returns while avoiding risks.Firstly,from the perspective of portfolio investment,this paper introduces the traditional Markowitz mean-variance model and capital asset pricing model(CAPM),then selects four funds from different industries by MATLAB program in Sina Finance and Economics Network for application analysis from which the optimal portfolio point can be obtained under the combination of efficient frontier and capital allocation line.Subsequently,by analyzing the returns of long-term holdings and short-term operations of Noan Growth Hybrid Fund,it is confirmed that long-term holding funds can better cope with the changing market so as to obtain more stable returns.Finally,this paper discusses the dynamic adjustments of asset portfolio.Resident investors are supposed to take into account the market situation and the changes of the fund itself to adjust the holding fund portfolio.Based on the research in this paper,resident investors ought to combine investment funds to diversify risk allocation and make long-term holding plans according to their risk tolerance.At the same time,they should also make appropriate dynamic adjustments when the external environment changes to ensure long-term benefits.

Time-consistent investment-reinsurance strategies towards joint interests of the insurer and the reinsurer under CEV models

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.

The Stochastic Maximum Principle for a Jump-Diffusion Mean-Field Model Involving Impulse Controls and Applications in Finance

This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control.The authors also show the existence and uniqueness of the solution to a jump-diffusion mean-field stochastic differential equation involving impulse control.As for its application,a mean-variance portfolio selection problem has been solved.