Portfolio analysis—an analytic derivation of the efficient portfolio frontier

In this paper the efficient portfolio frontier is derived explicitly for cases in which short sales are not allowed. When all securities are risky it is shown that the efficient portfolio frontier consist of a series of monotonously increasing arcs of convex parabolas in the return-variance plane. If the efficient portfolio frontier of risky securities are known, the efficient frontier can easily be revealed when there is a riskless security. An upper limit on borrowing is also introduced.     

Optimal investment consumption model with a higher interest rate for borrowing

This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate. Wealth is divided into a riskless asset and risky asset with logrithmic Erownian motion price fluctuations. The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied. Equivalent conditions for optimality are obtained. By using duality methods ,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.     

Portfolio adjusting optimization with added assets and transaction costs based on credibility measures

In response to changeful financial markets and investor’s capital, we discuss a portfolio adjusting problem with additional risk assets and a riskless asset based on credibility theory. We propose two credibilistic mean–variance portfolio adjusting models with general fuzzy returns, which take lending, borrowing, transaction cost, additional risk assets and capital into consideration in portfolio adjusting process. We present crisp forms of the models when the returns of risk assets are some deterministic fuzzy variables such as trapezoidal, triangular and interval types. We also employ a quadratic programming solution algorithm for obtaining optimal adjusting strategy. The comparisons of numeral results from different models illustrate the efficiency of the proposed models and the algorithm.     

Portfolio adjusting optimization with added assets and transaction costs based on credibility measures

In response to changeful financial markets and investor’s capital, we discuss a portfolio adjusting problem with additional risk assets and a riskless asset based on credibility theory. We propose two credibilistic mean–variance portfolio adjusting models with general fuzzy returns, which take lending, borrowing, transaction cost, additional risk assets and capital into consideration in portfolio adjusting process. We present crisp forms of the models when the returns of risk assets are some deterministic fuzzy variables such as trapezoidal, triangular and interval types. We also employ a quadratic programming solution algorithm for obtaining optimal adjusting strategy. The comparisons of numeral results from different models illustrate the efficiency of the proposed models and the algorithm.     

关于无风险资产不存在时资产组合选择的研究

以往关于资产组合选择的研究大多假设市场上存在无风险资产,但无风险资产实际上是不存在的.当不存在无风险资产时,假设投资者的效用定义在消费上,消费一直是投资者财富的一个固定比例,投资者的最优资产组合由两部分组成:短视的资产组合和对冲组合.假设只有股票和债券两种风险资产,当股票和债券的风险具有负的相关性时,投资者现在会消费更多,同时也会在股票上投资更多;两者正相关时,投资者无法降低风险,会减持股票并降低当前消费;两者不相关时,投资者持有的股票权重和存在无风险资产时一样.最后,还推导出了多种资产情况下最优消费和资产组合的解析表达式.     

不具有与具有卖空限制的证券选择理论(英文)

本文讨论不具有与具有卖空限制的证券选择理论．不具有卖空限制的证券选择问题作为规划问题用Lagrange数法求解．这个问题可以推广到具有卖空限制情形．用Kuhn－Tucker条件求解．     

Optimal portfolio strategies with a liability and random risk: The case of different lending and borrowing rates

This paper deals with two problems of optimal portfolio strategies in continuous time. The first one studies the optimal behavior of a firm who is forced to withdraw funds continuously at a fixed rate per unit time. The second one considers a firm that is faced with an uncontrollable stochastic cash flow, or random risk process. We assume the firm’s income can be obtained only from the investment in two assets: a risky asset (e.g., stock) and a riskless asset (e.g., bond). Therefore, the firm’s wealth follows a stochastic process. When the wealth is lower than certain legal level, the firm goes bankrupt. Thus how to invest in the fundamental problem of the firm in order to avoid bankruptcy. Under the case of different lending and borrowing rates, we obtain the optimal portfolio strategies for some reasonable objective functions that are the piecewise linear functions of the firm’s current wealth and present some interesting proofs for the conclusions. The optimal policies are easy to be operated for any relevant investor.     

Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity

We consider the problem of optimal portfolio choice using the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures for a market consisting of n risky assets and a riskless asset and where short positions are allowed. When the distribution of returns of risky assets is unknown but the mean return vector and variance/covariance matrix of the risky assets are fixed, we derive the distributionally robust portfolio rules. Then, we address uncertainty (ambiguity) in the mean return vector in addition to distribution ambiguity, and derive the optimal portfolio rules when the uncertainty in the return vector is modeled via an ellipsoidal uncertainty set. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction.     

On the distribution tail of an integrated risk model: A numerical approach

We consider an insurance risk process with the possibility to invest the capital reserve into a portfolio consisting of a risky asset and a riskless asset. The stock price is modelled by an exponential Lévy process and the riskless interest rate is assumed to be constant. We aim at the risk assessment of the integrated risk process in terms of a high quantile or the far out distribution tail. We indicate an application to an optimal investment strategy of an insurer.     

证券数减少情形下M—V证券组合特征灵敏度分析

本文研究当市场不存在无风险收益证券且允许卖空时证券组合特征关于证券数减少的灵敏度分析,给出了有效边缘、渐近线斜率、全局最小方差证券组合及其协方差、最小方差证券组合的投资权数、最小方差证券组合之间结合线等的变化模式,得到了一些有意义的结果．这不仅是对证券组合选择理论的进一步完善,对投资者也具有一定的指导意义     

Multi-stock portfolio optimization under prospect theory

We study how a behavioral agent allocates her portfolio. We consider a cumulative prospect theory investor in a single period setting with one riskless bond and multiple risky stocks, which follow a multivariate elliptical distribution. Our main result is a two-fund separation between the riskless bond and a mean?Cvariance-portfolio, up to an exogenous benchmark portfolio. The mean?Cvariance-portfolio, which we derive explicitly, is the same for all agents. Individual risk preferences are mirrored only in the participation in this portfolio. This dependence is illustrated by considering empirical returns. Furthermore we solve ill-posed optimization problems by imposing a regulatory risk constraint. Finally we address specific parameterizations of the value function by studying power, linear, and exponential utility.     

The role of longevity bonds in optimal portfolios

We study the optimal consumption and portfolio for an agent maximizing the expected utility of his intertemporal consumption in a financial market with: (i) a riskless asset, (ii) a stock, (iii) a bond as a derivative on the stochastic interest rate, and (iv) a longevity bond whose coupons are proportional to the population (stochastic) survival rate. With a force of mortality instantaneously uncorrelated with the interest rate (but not necessarily independent), we demonstrate that the wealth invested in the longevity bond must be taken from the ordinary bond and the riskless asset proportionally to the duration of the two bonds. This result is valid for both a complete and an incomplete financial market.     

均值方差偏好和期望损失风险约束下的动态投资组合

本文在均值方差框架下,研究了期望损失风险约束下的连续时间动态投资组合问题。运用鞅理论和凸对偶方法,分别给出了最优财富和最优投资策略的解析式,而且两基金分离定理仍然成立。最后通过数值例子分析了风险约束对最优投资策略的影响。     

贝叶斯方法在养老基金资产负债管理中的应用

把一个静态资产负债管理模型———均值方差模型应用到定额给付养老金计划的资产负债管理中,在允许无风险借贷的条件下研究养老金在无风险资产和风险资产间的分配问题,用定量分析的方法求出了最优投资组合的一般形式;又针对投资收益率特征参数未知的情况,提出了矩估计和贝叶斯估计两种方法求解最优资本配置比例,将两种方法的结果与一般形式对比,分析了影响最优投资组合的因素,得知养老基金在风险资产中的投资比例与基金经理对风险的厌恶程度、风险资产的风险益酬、风险资产收益率的波动性成负相关关系;并且随决策者掌握的历史信息增加,在风险资产上的投资比例也随之增加,投资行为逐渐趋于理性化;对上述结果进行仿真,验证了结论的有效性。     

Contingent claim valuation in a market with different interest rates

The problem of contingent claim valuation in a market with a higher interest rate for borrowing than for lending is discussed. We give results which cover especially the European call and put options. The method used is based on transforming the problem to suitable auxiliary markets with only one interest rate for borrowing and lending and is adapted from a paper of Cvitanic and Karatzas (1992) where the authors study constrained portfolio problems.     

Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.     

A note on portfolios with risk-free internal gains

In this paper we show that if a not-necessarily-self-financing portfolio has instantaneously riskless internal gains, then on an infinitesimal time-interval, the increase in the internal gains on the portfolio is the same as the change in the price of that amount of bonds which has the same wealth as the portfolio has. As an application of this result, we derive the Black–Scholes PDE by using the original derivation of Black and Scholes, and we show that it can be made completely rigorous.     

An analytic derivation of admissible efficient frontier with borrowing

The admissible efficient portfolio selection problem for risky assets has been discussed by Zhang and Nie. In this paper, the admissible efficient portfolio model is proposed under the assumption that there exists the borrowing (money or a risk free asset) case. The admissible efficient frontiers are developed by the spreads of expected return and risk from admissible errors. The analytic forms of the admissible efficient frontiers when short sales are not allowed on all risky assets are derived from two cases: the borrowing with an upper bound constraint, or without an upper bound constraint. The influence on the admissible efficient frontier is explained under the different interest rates of the borrowing. The differences between the results with the borrowing and the results without the borrowing is revealed by a real numerical example.     

无风险资产有限借入的不相关证券组合有效集的解析表示

本文研究了不允许卖空条件下存在无风险资产有借入的不相关证券有效组合问题,给出了有效集及投资比例的解析表示。     

t-分布与不同风险度量下有效投资组合及其边缘的相互关系研究

In order to study the effect of different risk measures on the efficient portfolios (frontier) 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.