On the rate of convergence of the St. Petersburg game

We investigate the repeated and sequential portfolio St. Petersburg games. For the repeated St. Petersburg game, we show an upper bound on the tail distribution, which implies a strong law for a truncation. Moreover, we consider the problem of limit distribution. For the sequential portfolio St. Petersburg game, we obtain tight asymptotic results for the growth rate of the game.     

证券投资组合优化问题的强健性的锥优化方法(英)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model

In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assuming infinitely divisible distributions, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal VaR and the marginal AVaR. We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average, first statistically validating the model based on goodness-of-fit tests and then demonstrating how the marginal VaR and marginal AVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a more tractable method for portfolio optimization.     

证券投资组合优化问题的强健性的锥优化方法(英文)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

Novel approaches for portfolio construction using second order stochastic dominance

In the last decade, a few models of portfolio construction have been proposed which apply second order stochastic dominance (SSD) as a choice criterion. SSD approach requires the use of a reference distribution which acts as a benchmark. The return distribution of the computed portfolio dominates the benchmark by the SSD criterion. The benchmark distribution naturally plays an important role since different benchmarks lead to very different portfolio solutions. In this paper we describe a novel concept of reshaping the benchmark distribution with a view to obtaining portfolio solutions which have enhanced return distributions. The return distribution of the constructed portfolio is considered enhanced if the left tail is improved, the downside risk is reduced and the standard deviation remains within a specified range. We extend this approach from long only to long-short strategies which are used by many hedge fund and quant fund practitioners. We present computational results which illustrate (1) how this approach leads to superior portfolio performance (2) how significantly better performance is achieved for portfolios that include shorting of assets.     

Integrated portfolio management with options

In this paper we examine the problem of managing portfolios consisting of both, stocks and options. For the simultaneous optimization of stock and option positions we base our analysis on the generally accepted mean–variance framework. First, we analyze the effects of options on the mean–variance efficient frontier if they are considered as separate investment alternatives. Due to the resulting asymmetric portfolio return distribution mean–variance analysis will be not sufficient to identify optimal optioned portfolios. Additional investor preferences which are expressed in terms of shortfall constraints allow a more detailed portfolio specification. Under a mean–variance and shortfall preference structure we then derive optioned portfolios with a maximum expected return. To circumvent the technical optimization problems arising from stochastic constraints we use an approximation of the return distribution and develop economically meaningful conditions under which the complex optimization problem can be transformed into a linear problem being comparably easy to solve. Empirical results based on both, empirical market data and Monte Carlo simulations, illustrate the portfolio optimization procedure with options.     

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.     

条件风险下的两基金分离定理

鉴于条件风险价值CVaR具有风险度量的合理性以及两基金分离定理对证券投资的重要意义,以CVaR作为风险度量研究两基金分离定理.在组合收益率服从正态分布的假设下,分别就投资组合含有或没有无风险资产的情形提出并证明了两基金分离定理;放开方差-协方差矩阵为非奇异这一通常假设,证明了CVaR风险度量下的两基金分离定理依然成立.     

Taylor series approximations to expected utility and optimal portfolio choice

This paper revisits the subject of Taylor series approximations to expected utility and investigates the applicability of the technique to optimal portfolio choice problems. We first provide conditions under which the approximate expected utility of a given portfolio converges to its exact counterpart. We then extend the analysis to the optimal portfolio choice setting and provide conditions on the distribution of asset returns under which the solution to the approximate portfolio choice problem converges to its exact counterpart. Finally, we show that, when asset returns are skewed, one can improve the precision and efficiency of the Taylor expansion by applying a simple nonlinear transformation to asset returns designed to symmetrize the transformed return distribution and shrink its support.     

A closed-form solution of the Black–Litterman model with conditional value at risk

We consider a portfolio optimization problem of the Black–Litterman type, in which we use the conditional value-at-risk (CVaR) as the risk measure and we use the multi-variate elliptical distributions, instead of the multi-variate normal distribution, to model the financial asset returns. We propose an approximation algorithm and establish the convergence results. Based on the approximation algorithm, we derive a closed-form solution of the portfolio optimization problems of the Black–Litterman type with CVaR.     

Portfolio selection under distributional uncertainty: A relative robust CVaR approach

Robust optimization, one of the most popular topics in the field of optimization and control since the late 1990s, deals with an optimization problem involving uncertain parameters. In this paper, we consider the relative robust conditional value-at-risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set. Our approach not only takes into account the worst-case scenarios of the uncertain distribution, but also pays attention to the best possible decision with respect to each realization of the distribution. We also illustrate how to construct a robust portfolio with multiple experts (priors) by solving a sequence of linear programs or a second-order cone program.     

A mean-absolute deviation-skewness portfolio optimization model

It is assumed in the standard portfolio analysis that an investor is risk averse and that his utility is a function of the mean and variance of the rate of the return of the portfolio or can be approximated as such. It turns out, however, that the third moment (skewness) plays an important role if the distribution of the rate of return of assets is asymmetric around the mean. In particular, an investor would prefer a portfolio with larger third moment if the mean and variance are the same. In this paper, we propose a practical scheme to obtain a portfolio with a large third moment under the constraints on the first and second moment. The problem we need to solve is a linear programming problem, so that a large scale model can be optimized without difficulty. It is demonstrated that this model generates a portfolio with a large third moment very quickly.Presently at Mitsubishi Trust Bank Co., Ltd.     

基于区间分析的投资组合VaR计算新方法

基于区间分析估计变量的累计概率分布是进行风险价值分析的一种新方法。本文将区间分析运用到股票投资组合的VaR计算中,研究区间分析在VaR计算方法中的应用。首先给出了基于区间分析估计分布函数的计算步骤,然后将区间分析运用到VaR的计算中,以两只股票的投资组合为例得出收益率的累计概率分布,从中得到某一置信度下的VaR值,最后与蒙特卡洛模拟方法做了比较研究,结果表明,基于区间分析的VaR计算方法的运算精度和计算速度明显优于蒙特卡洛模拟方法。     

损失厌恶偏好与资产组合选择研究

在不确定性条件下,期望的不可计算性、行动结果比较的局限性以及投资个体选择的非理性使理性假定的选择理论脱离现实,因此重新探讨决策选择准则是必要的.以行为金融理论中不确定性状态下的有限理性与满意准则为依据,引入与满意准则一致且体现损失厌恶偏好的VaR作为风险指标,构建行为资产组合模型,在一种简单新颖的M-V模型的矩阵解法基础上,探寻了正态与部分非正态性假设下VaR-BPT模型的显性最优解或有效前沿,解决了现实中最优投资组合选择的可操作性难题,并在中国股票市场验证了正态性转换方法是处理非正态分布下资产组合选择问题的一种优秀方法.     

Robust portfolio optimization with copulas

Conditional Value at Risk (CVaR) is widely used in portfolio optimization as a measure of risk. CVaR is clearly dependent on the underlying probability distribution of the portfolio. We show how copulas can be introduced to any problem that involves distributions and how they can provide solutions for the modeling of the portfolio. We use this to provide the copula formulation of the CVaR of a portfolio. Given the critical dependence of CVaR on the underlying distribution, we use a robust framework to extend our approach to Worst Case CVaR (WCVaR). WCVaR is achieved through the use of rival copulas. These rival copulas have the advantage of exploiting a variety of dependence structures, symmetric and not. We compare our model against two other models, Gaussian CVaR and Worst Case Markowitz. Our empirical analysis shows that WCVaR can asses the risk more adequately than the two competitive models during periods of crisis.     

Multi-objective possibilistic model for portfolio selection with transaction cost

In this paper, we introduce the possibilistic mean value and variance of continuous distribution, rather than probability distributions. We propose a multi-objective Portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation. For quantifying any potential return and risk, portfolio liquidity is taken into account and a multi-objective non-linear programming model for portfolio rebalancing with transaction cost is proposed. The models are illustrated with numerical examples.     

一类重尾风险因子的模拟及其投资高风险值和置信区间的估计

由于金融市场中的日周期或短周期对数回报率的样本数据多数呈现胖尾分布，于是现有的正态或对数正态分布模型都在不同程度上失效，为了准确模拟这种胖尾分布和提高投资风险估计及金融管理，本文引进了一种可根据实际金融市场数据作出调正的蒙特卡洛模拟方法．这个方法可以有效地复制金融产品价格的日周期对数回报率数据的胖尾分布．结合非参数估计方法，利用该模拟方法还得到投资高风险值以及高风险置信区间的准确估计。     

基于Clayton Copula-GARCH模型投资组合VaR的度量

运用Copula方法研究了含股指期货的投资组合的风险度量问题.首先采用不同的GARCH模型对单个资产收益率建模,然后选择Clayton Copula函数来描述投资组合各资产之间的相关结构,建立联合分布模型,进而采用Monte Carlo方法模拟产生各资产的收益率序列,计算出投资组合的VaR.Kupiec检验表明,ClaytonCopula-GARCH模型在投资组合风险度量上具有较高的准确性.     

二阶随机占优约束下考虑偏度的投资组合模型

在DentchevaRuszczynski(2006)模型的基础上,考虑偏度对构建投资组合的影响,建立了二阶随机占优约束下最大化组合收益率偏度的投资组合优化模型,并应用分段线性近似方法将模型转化为一个非线性混合整数规划问题.利用中国股票市场的历史数据对所建模型进行了实证分析,结果表明,所建新模型比均值-方差-偏度模型和市场指数具有更稳健的表现.     

Credit contagion in a network of firms with spatial interaction

This contribution studies the effects of credit contagion on the credit risk of a portfolio of bank loans. To this aim we introduce a model that takes into account the counterparty risk in a network of interdependent firms that describes the presence of business relations among different firms. The location of the firms is simulated with probabilities computed using an entropy spatial interaction model. By means of a wide simulation analysis we investigate the behavior of the model proposed and study the effects of default contagion on the loss distribution of a portfolio of bank loans.