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.

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.

Multistage Stochastic Programming Model for the Portfolio Problem of a Property-Liability Insurance Company

The current portfolio model for property-liability insurance company is only single period that can not meet the practical demands of portfolio management, and the purpose of this paper is to develop a multiperiod model for its portfolio problem. The model is a multistage stochastic programming which considers transaction costs, cash flow between time periods, and the matching of asset and liability; it does not depend on the assumption for normality of return distribution. Additionally, an investment constraint is added. The numerical example manifests that the multiperiod model can more effectively assist the property-liability insurer to determine the optimal composition of insurance and investment portfolio and outperforms the single period one.

A branch-and-bound algorithm for discrete multi-factor portfolio optimization model

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.

Application of Portfolio Model in the Real Investment Transactions

This paper studies discrete investment portfolio model that the objective function is utility function. According to a hybrid branch-and-bound method based on Lagrangian relaxation and continuous relaxation, the paper analyzes the question using the real statistical data. The results indicate that discrete investment portfolio model really has its guidance in the actual investment.

Stochastic Modelling on Dynamics of Portfolio Diversifications among the Fixed and Operational Investments through Internal Bivariate Linear Birth, Death and Migration Processes

In this paper, a bivariate stochastic process with Poisson postulates has been considered to model the incomings, outgoings and mutual transfers of investments between and within the portfolios during an epoch of time “t”. Stochastic differential equations were obtained from the simple differential difference equations during the epoch of time “Δt”. The notion of bivariate linear birth, death and migration process has been utilized for measuring various statistical characteristics among the investments of Long and Short terms. All possible fluctuations in the investment flow have been considered to explore more meaningful assumptions with contemporary marketing environments. Mathematical relations for proposed statistical measures such as average sizes and variances of short term and long-term investments along with the correlation coefficient between them are derived after obtaining the related differential equations. Numerical illustrations were provided for better understanding of the developed models with practitioner’s point of view.

Bounds for Goal Achieving Probabilities of Mean-Variance Strategies with a No Bankruptcy Constraint

We establish, through solving semi-infinite programming problems, bounds on the probability of safely reaching a desired level of wealth on a finite horizon, when an investor starts with an optimal mean-variance financial investment strategy under a non-negative wealth restriction.

Dynamic Portfolio Choice under Uncertainty about Asset Return Model

The effect of uncertainty about stochastic diffusion model on dynamic portfolio choice of an investor who maximizes utility of terminal portfolio wealth was studied.It applied stochastic control method to obtain the closed-form solution of optimal dynamic portfolio,and used the Bayesian rule to estimate the model parameters to do an empirical study on two different samples of Shanghai Exchange Composite Index.Results show,model uncertainty results in positive or negative hedging demand of portfolio,which depends on investor's attitude toward risk;the effect of model uncertainty is more significant with the increasing of investment horizon,the decreasing of investor's risk-aversion degree,and the decreasing of information;predictability of risky asset return increases its allocation in portfolio,at the same time,the effect of model uncertainty also strengthens.

Multi-Knapsack Model of Collaborative Portfolio Configurations in Multi-Strategy Oriented

Aiming at constructing the multi-knapsack model of collaborative portfolio configurations in multi-strategy oriented, the hybrid evolutionary algorithm was designed based on greedy method, combining with the organization of the multiple strategical guidance and multi-knapsack model. Furthermore, the organizing resource utility and risk management of portfolio were considered. The experiments were conducted on three main technological markets which contain communication, transportation and industry. The results demonstrated that the proposed model and algorithm were feasible and reliable.

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.

Expanded models of the project portfolio selection problem with learning effect

This research develops two new models for project portfolio selection, in which the candidate projects are composed of multiple repetitive units. To reflect some real situations, the learning effect is considered in the project portfolio selection problem for the first time. The mathematical representations of the relationship between learning experience and investment cost are provided. One numerical example under different scenarios is demonstrated and the impact of considering learning effect is then discussed.

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.

Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon

This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion.The Markov chain is assumed to be independent of Brownian motion,thus the market is incomplete.The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem.The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier.All the results are different from those in the problem with fixed time horizon.

Schedule Model for Project Portfolio Based on Design Structure Matrix

To improve the enterprise resource utilization and shorten the cycle of the whole project portfolio, a scheduling model based on Design Structure Matrix （DSM） is built. By setting the project activity weight index system and calculating the activity weight for the project portfolio, the constraint relationship between project portfolio information and resource utilization, as the two dimensions of the DSM, are fully reflected in the sched- ule model to determine the order of these activities of project portfolio. A project portfolio example is given to il- lustrate the applicability and effectiveness of the schedule model.

Copula模型的改进及其应用

Copula模型能精确计算投资组合尾部风险,弥补Person相关系数的不足。文章基于信用风险Cop⁃ula模型,探讨了不同抽样算法在信贷投资组合中的应用问题,优化重要性抽样和交叉熵算法,测试了高斯及t-Copula模型的风险计算算法,并通过数值模拟予以检验,结果表明:朴素蒙特卡罗模拟的精度和效率较低;重要性抽样算法通过解析逼近显著降低计算方差,提高精度,但求解复杂且耗时;交叉熵算法同样有效,但需自适应算法求解优化问题。算例分析结果表明,基于不同场景选择Copula模型,可提高信贷投资组合风险计算精度和效率。

Heston模型下的两人鲁棒非零和随机微分投资组合博弈

用Heston模型描述风险资产的价格动态,构建了包含一种无风险资产和一种风险资产的金融市场,投资者可以将其财富自由地配置于无风险资产和风险资产中.考虑到投资者之间经济行为的随机博弈,用相对业绩刻画投资者之间的博弈行为,同时考虑模型的不确定性,以最大化最坏情境下投资者相对业绩的期望效用为目标,构建了包含两个投资者的鲁棒非零和随机微分投资组合博弈模型,利用动态规划方法分别求得了CRRA效用下Nash均衡策略的解析表达,借助数值仿真算例进行了参数的敏感性分析并给出了相应的经济意义阐释.研究发现:相较于不涉及市场竞争的传统投资策略,竞争将使投资者产生羊群效应,跟风投资风险资产,致使金融市场的系统性风险上升.此外,与不考虑模型不确定性相比,模型的不确定性使得投资者减少对风险资产的投资.

工程项目组合风险扩散模型的级联失效分析

为构建符合工程项目组合特点的风险扩散模型,解决风险扩散问题。本文考虑风险扩散的双关系载体—项目交互关系和风险因素逻辑关系,构建工程项目组合风险扩散的双层相依网络模型,运用级联失效理论提出风险扩散规则,通过数值仿真分析风险扩散特征。仿真结果发现:工程项目组合中,双层网络模型能够反映风险在项目和风险因素双关系载体中的扩散特征;与单层网络风险扩散模型相比,构建的模型展现出差异性的风险扩散效应,风险扩散在工程项目组合中表现出更剧烈的级联失效过程。风险扩散模型作为工程项目组合风险扩散问题的前置性研究,为进一步风险扩散网络稳定性的研究提供新思路和启发。