Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment

We propose a possibilistic portfolio model with VaR constraint and risk-free investment based on the possibilistic mean and variance, while assuming that the expected rate of returns is a fuzzy number. The model shows more clearly that, in the financial market affected by several non-probabilistic factors, risk-averse investors wish not only to reach the expected rate of returns in their actual investment, but also to assure that the maximum of their possible future risk is lower than an expected loss. Under the condition that the expected rate of returns is a normal distribution fuzzy variable, we proposed a theorem as the solution, and derive a crisp equivalent form of the possibilistic portfolio under constraints of VaR and risk-free investment. This model is an expansion of the fuzzy possibilistic mean–variance model by Zhang (2007). Finally, an empirical study is carried out using the data concerning some stocks of various industries listed at the Shanghai Stock Exchange. A conclusion is reached that the investors are able to choose a portfolio more suitable to them under the VaR constraint.     

基于截集的加权可能性均值-方差模型

本文以模糊数的截集为切入点,给出随机变量取值为模糊数时基于截集的加权可能性均值、加权可能性方差和加权可能性协方差的定义,研究了基于截集的加权可能性均值、加权可能性方差和加权可能性协方差的性质,给出三角模糊数的基于截集的加权可能性均值、加权可能性方差和加权可能性协方差的具体形式.并以基于截集的加权可能性均值作为证券组合投资收益率为模糊数时投资未来收益的度量,以基于截集的加权可能性方差作为证券组合投资收益率为模糊数时投资风险的度量,以基于截集的加权可能性协方差作为不同资产之间相关程度的度量,以不同的权重表示不同投资者的对投资收益的风险偏好程度,构建基于模糊数截集的加权可能性均值-方差组合投资模型,给出模型的求解方法.最后将基于截集的加权可能性均值-方差模型与传统的均值-方差模型进行了比较分析,并结合我国证券交易市场的具体实例说明该模型的应用价值.     

A multi-period portfolio selection optimization model by using interval analysis

Due to few historical data that can be obtained in an emerging securities market, the future returns, risk and liquidity of securities cannot be forecasted precisely. The investment environment is usually fuzzy and uncertain. To handle these imprecise data, this paper discusses a fuzzy multi-period portfolio optimization problem where the returns, risk, and liquidity of securities are represented by interval variables. By taking the return, risk, liquidity and diversification degree of portfolio into consideration, an interval multi-period portfolio selection optimization model is proposed with the objective of maximizing the terminal wealth under the constraints of the return, risk and diversification degree of portfolio at each period. In the proposed model, a proportion entropy is employed to measure the diversification degree of portfolio. Using the fuzzy decision-making theory and multi-objective programming approach, the proposed model is transformed into a crisp nonlinear programming. Then, we design an improved particle swarm optimization algorithm for solution. Finally, a numerical example is given to illustrate the application of our model and demonstrate the effectiveness of the designed algorithm.     

Multi-period Markowitz's mean–variance portfolio selection with state-dependent exit probability

This paper considers a multi-period mean–variance portfolio selection problem with uncertain time-horizon in a regime-switching market, where the conditional distribution of the time-horizon is assumed to be stochastic and depends on the market states as the returns of risky assets do. Existence of the optimal investment strategy is analyzed, and the closed-form expressions for the optimal investment strategy and the efficient frontier are derived. In addition, some interesting properties of the efficient frontier are illustrated by numerical analysis and by comparing with the efficient frontier of the case where the distribution of the uncertain time-horizon does not depend on market states.     

Evolution,finance, and the population genetics of relative wealth

Attempts to use evolutionary ideas in finance have often neglected mathematical population genetics. Population genetics provides a natural approach to certain problems in finance that involve the relative wealth that accrues to competing investment strategies. In our model, competing investment strategies differ only in their allocation to a risky asset versus a riskless asset. Here we use results from the population genetics of natural selection to find the investment strategy that maximizes the expected increase in relative wealth. Though we focus on single-period analysis, some of our key findings are reminiscent of those from the growth optimal portfolio literature, e.g., the Kelly criterion.     

A possibilistic portfolio adjusting model with new added assets

In order to fit changes in financial markets, portfolio managers often need to revise an existing portfolio. This article analyzes the portfolio adjusting problem with new added assets. We propose a possibilistic portfolio adjusting model with transaction costs and bounded constraints on holdings of assets, which can be transformed into a linear programming problem. Both the lower bounds on holdings and the total investment constraints influence the optimal portfolio adjusting strategies. Furthermore, a numerical example of a portfolio adjusting problem is given to illustrate our proposed effective approaches. The numerical results show the case that investors do not need to invest total capital and to hold all assets in the portfolio for some required return levels.     

A risk index to model uncertain portfolio investment with options

This paper models the portfolio investment performance with options by using a risk index, which is defined as the average loss below the risk-free interest rate. Using a risk-free interest rate as the uniform reference rate for all portfolios, the risk index offers an easier-to-compare loss value than the value-at-risk return, where portfolio specific references are used to calculate the average losses. Besides, uncertainty theory is used in the paper to derive the portfolio decision when stock prices are subject to experts' estimations. By analytical computation and empirical analysis, we find that portfolios considering options generate better return than the ones without options. The empirical analysis reveals that the options can effectively hedge the risk, and the call option with a higher exercise price offers higher return per unit of option premium. Furthermore, our proposed model produces higher expected return in most cases than the model where the risk is measured by the chance of the total return failing to reach the threshold level of return.     

基于FANP方法的专利组合价值评估模型设计及应用研究——以“深圳大疆”为例

持续加剧的中美贸易摩擦及知识产权争端,深刻揭示了企业增加研发投入的紧迫性以及专利技术促进企业持续发展的重要性,企业专利竞争已从单项专利转向组合专利进一步凸显了专利组合价值。基于价值理论和专利战略理论,提出将技术价值、市场价值、法律价值作为专利组合价值评估一级指标。在此基础上,通过单项专利和组合专利的特征分析,结合企业国际化理论和专利标准化内涵,提出相应的二级指标。考虑到决策者的主观性和模糊性、评价指标之间的依赖关系与反馈机制,采用模糊网络分析法（FANP）构建专利组合价值评估模型,运用企业专利组合实际数据进行测算以验证评估模型的合理性和实用性。结果发现：高质量专利组合对企业价值有非常显著的贡献度;企业应定期评估以调整优化专利组合结构,提升专利资产的整体价值、增强企业竞争优势;专利组合价值是衡量企业知识产权战略绩效的重要评价指标,从大数据视角构建专利组合价值评估模型是值得进一步研究的问题。     

On trees and logs

In this paper we contrast the main workhorse model in asset pricing theory, the Lucas (1978) tree model (LT-Model), to a benchmark model in financial equilibrium theory, the real assets model (RA-Model). It is commonly believed that the two models entail similar conclusions since the LT-Model is a special case of the RA-Model. But this is simply wrong: implications of these models can be strikingly at odds. Indeed, under the widely used log-linear specification of households’ preferences, we show that for a large set of initial endowments the LT-Model—even with potentially complete financial markets—admits only peculiar financial equilibria in which the stock market is completely degenerate, in that all stocks offer the same investment opportunity—and yet, allocation is Pareto optimal. We investigate why the LT-Model is so much at variance with the RA-Model, and uncover new results on uniqueness of financial equilibria and introduction of portfolio constraints obtaining in the LT-Model, but not in the RA-Model.     

Optimal project adjustment and selection

These days companies are competing in a fast changing environment. To keep its competitiveness, the company needs not only to seek and select new investment opportunities but also to adjust its existing projects. This paper discusses an optimal project selection and adjusting problem under capital and land resource limitations. Due to the complex and dynamic nature of the economic environment, the project parameters such as initial outlays, upgrade expenditures and net cash flows are treated as random variables. Net present value method is employed to calculate the investment return, and a mean–variance optimal adjustment and selection model is developed. To solve the proposed optimization problem with big number decision variables, a cellular binary particle swarm optimization which hybridizes cellular automation and particle swarm optimization is proposed. As an illustration of the proposed algorithm, a numerical example is also presented.     

Energy portfolio risk management using time-varying extreme value copula methods

This work is concerned with the statistical modeling of the dependence structure between three energy commodity markets (WTI crude oil, natural gas and heating oil) using the concept of copulas and proposes a method for estimating the Value at risk (VaR) of energy portfolio based on the combination of time series models with models of the extreme value theory before fitting a copula. Each return series is modeled by AR-(FI) GARCH univariate model. Then, we fit the GPD distribution to the tails of the residuals to model marginal residuals distributions. The extreme value copula to the iid residuals is fitted and we simulate from it to construct N portfolios and estimate VaR. As a first step, the method is applied to a two-dimensional energy portfolio. In second step, we extend method in trivariate context to measure VaR of three-dimensional energy portfolio. Dependences between residuals are modeled using a trivariate nested Gumbel copulas. Methods proposed are compared with various univariate and multivariate conventional VaR methods. The reported results demonstrate that GARCH-t, conditional EVT and FIGARCH extreme value copula methods produce acceptable estimates of risk both for standard and more extreme VaR quantiles. Generally, copula methods are less accurate compared with their predictive performances in the case of portfolio composed of exchange market indices.     

Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns

This paper is concerned with linear portfolio value-at-risk (VaR) and expected shortfall (ES) computation when the portfolio risk factors are leptokurtic, imprecise and/or vague. Following Yoshida (2009), the risk factors are modeled as fuzzy random variables in order to handle both their random variability and their vagueness. We discuss and extend the Yoshida model to some non-Gaussian distributions and provide associated ES. Secondly, assuming that the risk factors' degree of imprecision changes over time, original fuzzy portfolio VaR and ES models are introduced. For a given subjectivity level fixed by the investor, these models allow the computation of a pessimistic and an optimistic estimation of the value-at-risk and of the expected shortfall. Finally, some empirical examples carried out on three portfolios constituted by some chosen French stocks, show the effectiveness of the proposed methods.     

基于模糊多准则群决策的可持续项目选择模型

将模糊多准则群决策方法应用于可持续项目的选择决策中。首先构建可持续项目选择框架,包括投资的经济、社会和环境影响以及战略联盟、组织准备和投资风险六个评价准则。由于该框架的准则权重很难通过一组决策者不一致的偏好而确定,所以,运用乘法偏好关系和模糊偏好关系收集决策者对准则权重的偏好,利用目标规划方法进行建模并确定各个准则的相对权重;然后用模糊TOPSIS方法评估投资机会的适合程度。TOPSIS方法是基于偏好比率的一种决策方法,其中偏好比率运用于模糊数排序和模糊距离测量,可以有效地计算出每个备选方案与理想方案的模糊距离,从而根据距离判断其亲密系数,并最终应用于最佳方案的抉择。最后,以某投资集团的可持续投资项目选择问题为例进行分析,验证了方法的有效性和可行性。     

Interval portfolio selection models within the framework of uncertainty theory

The expected returns for securities are traditionally estimated as crisp values. Since the improper values may bring on an unsuccessful investment decision, portfolio experts generally prefer offering interval estimations for expected returns rather than crisp ones. The portfolio selection problem with interval expected returns is widely studied recently. In this paper, by considering the security returns with interval expected returns as uncertain variables, a mean-semiabsolute deviation model is proposed within the framework of uncertainty theory, which is a crisp nonlinear programming model and can be well solved by the classical optimization algorithms. In order to illustrate the method, some numerical experiments are given and solved.     

The Wicksell-Tobin investment model

We formalize in this paper Wicksell's investment decision model and compare it with Tobin's q-theory. Wicksell's firms either compare the natural rate of interest with the prevailing market interest rate or the capital values with the replacement costs of investment projects. This exposition of Wicksell's approach reveals some striking similarities with Tobin's supply-price-of-capital model, which relates the marginal efficiency of capital to the rate of return required by portfolio investors in the well-known q-ratio. The ratio market value to replacement cost of capital should, therefore, more appropriately be termed the Wicksell-Tobin q. Our formalization of Wicksell's investment theory appears to open up a promising new avenue for further research in cases where banks provide the source of funds.     

Continuous-time mean–variance portfolio selection with only risky assets

We investigate in this paper a continuous-time mean–variance portfolio selection problem in a general market setting with multiple assets that all can be risky. Using the Lagrange duality method and the dynamic programming approach, we derive explicit closed-form expressions for the efficient investment strategy and the mean–variance efficient frontier. We provided a necessary and sufficient condition under which the global minimum variance is zero and there exists a risk-free wealth process. Our results reveal that, even if there is no risk-free asset in the market, there can still exist a risk-free wealth process, the global minimum variance can be zero, and the efficient frontier can be a straight line in the mean–standard derivation plane. In addition, we further prove the validity of the two-fund separation theorem.     

Real options and demographic decisions

The theory of real options is used to incorporate the influence of uncertainty on demographic decision-making. The decision to have children is formulated as an investment using portfolio theory. The timing of the decision to have a child is modelled as a real options decision, with uncertainty affecting a woman's ability to exercise the ‘option to wait’ in order to delay or space births. An increase and reduction in uncertainty on this option is explored. Compared to the widely used net present value (NPV) framework, the real options approach (ROA) better explains the process of demographic decision-making in poor countries.     

Dynamic risk management in petroleum project investment based on a variable precision rough set model

In this paper, an adaptive algorithm is designed for dynamic risk management in petroleum project investment based on a variable precision rough set (VPRS) model. In risk management, at each stage of decision-making, experts are invited to identify risk indices and support the decision-maker in evaluating the risk exposure (RE) of individual projects. The VPRS model is used to mine risk rules and determine the significance of risk indices from RE decision tables. Considering that there are multiple risks involved in any petroleum project investment, we use multi-objective programming to obtain the optimal selection of projects with minimum RE, where the significance of risk indices is assigned to each of the corresponding multi-objective functions as a weight. Moreover, we develop a risk ranking model to measure the degree of risk for individual projects in a portfolio. Finally, a numerical example based on a Chinese petroleum company's investments in overseas projects is presented to illustrate the proposed approach, and then conclusions are drawn.     

中国外汇储备投资多样化研究

2006年末，我国外汇储备已突破1万亿美元，远远超过了外汇储备的最优规模。从外汇储备“藏汇于国，，与“藏汇于民”的不同管理模式出发，在实证分析基础上，可以2003年为拐点，考察近年来我国存在外汇储备超额现象。根据资产组合理论和部分国家和地区外汇储备积极管理经验，提出相关策略。     

On mean-variance portfolio selection under a hidden Markovian regime-switching model

We study a mean-variance portfolio selection problem under a hidden Markovian regime-switching Black–Scholes–Merton economy. Under this model, the appreciation rate of a risky share is modulated by a continuous-time, finite-state hidden Markov chain whose states represent different states of an economy. We consider the general situation where an economic agent cannot observe the “true” state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes. By exploiting the separation principle, we discuss the mean-variance portfolio selection problem and the filtering-estimation problem separately. We determine an explicit solution to the mean-variance problem using the stochastic maximum principle so that we do not need the assumption of Markovian controls. We also provide robust estimates of the hidden state of the chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model. This simplifies the filtering-estimation problem.