部分信息下的最优投资选择模型研究

在部分信息下研究了均值方差投资选择模型.投资者只能观察到风险资产的价格,漂移过程用一个高斯过程来刻画.本文的目的是使最终财富期望最大化,而使得最终财富的方差最小.本文模型中有一个债券及股票资产,在部分信息下推导出了最优策略及均值方差有效前沿.     

引入成交量变化率的马柯维茨均值方差模型

对马柯维茨的均值方差理论进行了推广,进一步细化原模型中的风险。把成交量变化率的方差也视为一种风险,在收益率的方差中加入成交量变化率的方差,构成一种两者线性组合的新证券组合风险。讨论在给定一定收益率和成交量变化率的条件下使得新风险最小的优化求值问题。把原模型中没有无风险证券时的前沿证券曲线从双曲线（抛物线）推广到双叶双曲面（抛物面）,把含有无风险证券时的前沿证券曲线从直线推广到圆锥面,还得到了一系列相应结论。同时对股票投资最优组合选择问题进行实证检验。     

Optimal control with constrained total variance for Markov jump linear systems with multiplicative noises

We consider in this paper the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises (MJLS-mn for short). Our objective is to present an optimal policy for the problem of maximising the system's total expected output over a finite-time horizon while restricting the weighted sum of its variance to a pre-specified upper-bound value. We obtain explicit conditions for the existence of an optimal control law for this problem as well as an algorithm for obtaining it, extending previous results in the literature. The paper is concluded by applying our results to a portfolio selection problem subject to regime switching.     

随机利率下的均值-方差最小套期保值

均值-方差套期保值是套期保值的主要方法之一。不连续资产价格的均值-方差套期保值策略通常是在利率为非随机的情况下获得的。本文考虑在随机利率下,资产价格为特殊半鞅的均值-方差套期保值问题。通过适当的概率测度变换,将具有随机利率的情形简化为非随机利率情形,再利用Galtchouk-Kunita-Watanabe分解,获得了资产价格为一般的特殊半鞅,具有随机利率的的均值-方差套期保值策略。     

A class of continuous-time portfolio selection with liability under jump-diffusion processes

A continuous-time mean-variance portfolio selection model is formulated with multiple risky assets and one liability under discontinuous prices which follow jump-diffusion processes in an incomplete market. The correlations between the risky assets and the liability are considered. The corresponding Hamilton–Jacobi–Bellman equation of the problem is presented. The optimal dynamic strategy and the efficient frontier in closed forms are derived explicitly by using stochastic linear-quadratic control technique. Finally, the effects on efficient frontier under the value-at-risk constraint are illustrated.     

Markowitz-based portfolio selection with cardinality constraints using improved particle swarm optimization

This work presents particle swarm optimization (PSO), a collaborative population-based meta-heuristic algorithm for solving the Cardinality Constraints Markowitz Portfolio Optimization problem (CCMPO problem). To our knowledge, an efficient algorithmic solution for this nonlinear mixed quadratic programming problem has not been proposed until now. Using heuristic algorithms in this case is imperative. To solve the CCMPO problem, the proposed improved PSO increases exploration in the initial search steps and improves convergence speed in the final search steps. Numerical solutions are obtained for five analyses of weekly price data for the following indices for the period March, 1992 to September, 1997: Hang Seng 31 in Hong Kong, DAX 100 in Germany, FTSE 100 in UK, S&P 100 in USA and Nikkei 225 in Japan. The test results indicate that the proposed PSO is much more robust and effective than existing PSO algorithms, especially for low-risk investment portfolios. In most cases, the PSO outperformed genetic algorithm (GA), simulated annealing (SA), and tabu search (TS).     

Optimal portfolio selection in a Lévy market with uncontrolled cash flow and only risky assets

This article considers an investor who has an exogenous cash flow evolving according to a Lévy process and invests in a financial market consisting of only risky assets, whose prices are governed by exponential Lévy processes. Two continuous-time portfolio selection problems are studied for the investor. One is a benchmark problem, and the other is a mean-variance problem. The first problem is solved by adopting the stochastic dynamic programming approach, and the obtained results are extended to the second problem by employing the duality theory. Closed-form solutions of these two problems are derived. Some existing results are found to be special cases of our results.     

基于顾客退货的风险规避型双渠道供应链最优策略

在随机市场需求条件下,考虑风险规避型双渠道供应链中存在顾客退货时的最优决策问题,决策变量为两个渠道的商品售价和制造商批发价。以集中决策时的最优决策作为比较标杆,重点利用均值—方差方法分析了分散决策时风险规避型制造商和零售商的最优决策。结合灵敏度分析和数值试验,讨论了分散决策下的风险规避度,以及市场需求波动和顾客退货率对最优决策的影响。结果表明,高退货率不利于零售商、制造商及整个供应链的收益;风险规避度对收益的影响不是一成不变的,与需求波动大小有关;分散决策虽然引起了双边际效应,但制造商风险规避度的增加将降低双边际效应的负面影响。     

均值-方差模型与单指数模型的应用

介绍了马克维茨的均值-方差模型和威廉.夏普的单指数模型,指出均值-方差模型存在的不足和单指数模型对均值-方差模型进行改进的合理性.通过实例对2个模型进行实证研究,并用LINGO软件进行求解.结果表明:单指数模型可以减少计算量,并且有分散投资风险的作用.最后提出了模型改进的思路.     

A hybrid approach for portfolio construction: Combing two-stage ensemble forecasting model with portfolio optimization

Combining the stock prediction with portfolio optimization can improve the performance of the portfolio construction. In this article, we propose a novel portfolio construction approach by utilizing a two-stage ensemble model to forecast stock prices and combining the forecasting results with the portfolio optimization. To be specific, there are two phases in the approach: stock prediction and portfolio optimization. The stock prediction has two stages. In the first stage, three neural networks, that is, multilayer perceptron (MLP), gated recurrent unit (GRU), and long short-term memory (LSTM) are used to integrate the forecasting results of four individual models, that is, LSTM, GRU, deep multilayer perceptron (DMLP), and random forest (RF). In the second stage, the time-varying weight ordinary least square model (OLS) is utilized to combine the first-stage forecasting results to obtain the ultimate forecasting results, and then the stocks having a better potential return on investment are chosen. In the portfolio optimization, a diversified mean-variance with forecasting model named DMVF is proposed, in which an average predictive error term is considered to obtain excess returns, and a 2-norm cost function is introduced to diversify the portfolio. Using the historical data from the Shanghai stock exchange as the study sample, the results of the experiments indicate the DMVF model with two-stage ensemble prediction outperforms benchmarks in terms of return and return-risk characteristics.