基于在线理论的股票算法交易策略研究

运用在线理论研究多支股票算法交易策略。在El-Yaniv等人研究基础上,构造了单支股票买入问题的在线策略,证明该策略为最优在线策略;将构造的单支股票交易策略应用到多支股票交易策略问题中,设计了多支股票交易策略算法,并以每支股票收益加权进行投资组合;最后选择上证A股二十支股票从2009年到2012年的交易时间价格数据验证本文所提策略有效性。将20支股票随机抽取10支组成一组,选4组分别进行验证,结果表明本文所给策略对于任意选择的多支股票有较好收益。对交易周期分别选取10个偶数长度进行验证,发现交易周期为18天时平均收益最大,平均收益率为5.2%。     

A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation

We present a new approach to asset allocation with transaction costs. A multiperiod stochastic linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by the model that balances expected return and risk. Utilizing portfolio protection and dynamic hedging, an investment portfolio similar to an option-like payoff structure on the initial investment portfolio is characterized. The relative changes in the expected terminal wealth, worst case payoff, and risk aversion, are studied theoretically and illustrated using a numerical example. This model dominates a static mean-variance model when the optimal portfolios are evaluated by the Sharpe ratio. Received: August 15, 1999 / Accepted: October 1, 2000?Published online December 15, 2000     

Replication and shortfall risk in a binomial model with transaction costs

The shortfall risk is defined as the optimal mean value of the terminal deficit produced by a self-financing portfolio whose initial value is smaller than what is required to replicate a contingent claim. In this paper we look for an explicit expression for it, as well as for the optimal strategy, when the market model is a binomial model with proportional transaction costs. We first study replication of European claims which satisfy suitable assumptions. We then investigate the shortfall minimization problem in a framework very similar to that without transaction costs. The author thanks the referee for useful comments on an earlier version of the present paper.     

Super-replication under proportional transaction costs: From discrete to continuous-time models

In this paper, we study the problem of finding the minimal initial capital (i.e. super-replication value) needed in order to hedge (without risk) European contingent claims in a Markov setting under proportional transaction costs. The main result is that the cheapest (trivial) buy-and-hold strategy is optimal. Such a negative result has been derived previously in different contexts. First, we focus on discrete-time binomial models. We prove that the continuous-time limit of the super-replication value is the cost of the cheapest buy-and-hold strategy. Then, the result is proved in a multivariate continuous-time model with Brownian filtration. As a direct consequence, we obtain an explicit characterization of the hedging set, i.e. the set of all initial positions in the market assets from which the contingent claim can be hedged through some admissible portfolio strategy.     

基于成交量分解模型的改进VWAP策略

传统VWAP(交易量加权平均价格)策略通过拆分大额委托订单,跟踪市场成交均价,达到最小化冲击成本的目的,而准确预测成交量日内分布是运用VWAP策略的关键。通过详细考察现有的改进VWAP策略中成交量预测模型的建模方式和预测结果,发现由于无法分离成交量日内周期结构,现有模型样本依赖性较大且难以适用于多数股票。因此,本文从个股与市场成交量变化趋势的关系角度出发,推导个股成交量与市场趋势的关系,通过构造个股成交量关于市场因素的因子载荷,将日内成交量分解为市场共同部分和个股特殊部分,预测成交量日内分布并构建动态VWAP策略。实证结果表明新的成交量分解模型可以有效分离个股的成交量日内周期结构,在此基础上构造的改进VWAP策略不仅具有较为广泛的适用性,且跟踪误差减少幅度比现阶段同类型的改进VWAP策略更大,能更好的降低市场冲击成本。     

Efficient portfolios in financial markets with proportional transaction costs

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general multi-currency financial market model with proportional transaction costs. In our setting, transaction costs may be random, time-dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. We provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig (Rev Financ Stud 1:67–88, 1988) and Jouini and Kallal (J Econ Theory 66: 178–197, 1995). We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system that prices it. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading, and give a dual representation of it as the largest proportion of the market price necessary for all agents to reach the same expected utility level.     

Valuation and hedging of participating life-insurance policies under management discretion

The valuation and hedging of participating life insurance policies, also known as with-profits policies, is considered. Such policies can be seen as European path-dependent contingent claims whose underlying security is the investment portfolio of the insurance company that sold the policy. The fair valuation of these policies is studied under the assumption that the insurance company has the right to modify the investment strategy of the underlying portfolio at any time. Furthermore, it is assumed that the issuer of the policy does not setup a separate portfolio to hedge the risk associated with the policy. Instead, the issuer will use its discretion about the investment strategy of the underlying portfolio to hedge shortfall risks. In that sense, the insurer’s investment portfolio serves simultaneously as the underlying security and as the hedge portfolio. This means that the hedging problem can not be separated from the valuation problem. We investigate the relationship between risk-neutral valuation and hedging of these policies in complete and incomplete financial markets.     

Merton problem in a discrete market with frictions

We study the classical optimal investment and consumption problem of Merton in a discrete time model with frictions. Market friction causes the investor to lose wealth due to trading. This loss is modeled through a nonlinear penalty function of the portfolio adjustment. The classical transaction cost and the liquidity models are included in this abstract formulation. The investor maximizes her utility derived from consumption and the final portfolio position. The utility is modeled as the expected value of the discounted sum of the utilities from each step. At the final time, the stock positions are liquidated and a utility is obtained from the resulting cash value. The controls are the investment and the consumption decisions at each time. The utility function is maximized over all controls that keep the after liquidation value of the portfolio non-negative. A dynamic programming principle is proved and the value function is characterized as its unique solution with appropriate initial data. Optimal investment and consumption strategies are constructed as well.     

基于VaR的权变投资组合保险策略及在中国股市中的实证研究

传统的投资组合保险策略在投资期内全程进行保险操作,在熊市期间确能起到保险作用,但在牛市期间又会丧失部分收益.应用滤嘴法则设计了基于V aR的权变型投资组合保险策略,实证结果表明,该策略很好地起到了投资与保险的功能,能有效地进行市场风险的实时监控,为保险资金或保本型基金投资股市提供了有效的手段.     

基于VaR的权变投资组合保险策略及实证分析

传统的投资组合保险策略在投资期内全程进行保险操作,在熊市期间确能起到保险作用,但在牛市期间又会夹失部分收益。应用综合了VaR技术和滤嘴法则的VaR套补的权变投资组合保险策略,则能弥补上述缺憾,为保险资金或保本型基金投资股市提供了有效的投资手段。     

有交易成本的模糊最优化投资

本文针对交易成本在证券组合投资中的重要地位 ,提出了考虑交易成本 ,并兼顾收益与风险的模糊最优化投资模型 ,分析了交易成本对投资有效边界的影响 ,并给出了最优投资比例公式 .这对投资者进行投资有重要的理论与实践意义 .最后 ,通过释例进行了说明 .     

共同基金和无风险资产投资的最优策略

利用均值-方差模型,分析了非线性交易成本下的共同基金与无风险资产投资组合的有效边界和在一般的效用函数下讨论了投资者的最优投资策略.     

Convex duality in optimal investment under illiquidity

We study the problem of optimal investment by embedding it in the general conjugate duality framework of convex analysis. This allows for various extensions to classical models of liquid markets. In particular, we obtain a dual representation for the optimum value function in the presence of portfolio constraints and nonlinear trading costs that are encountered e.g. in modern limit order markets. The optimization problem is parameterized by a sequence of financial claims. Such a parameterization is essential in markets without a numeraire asset when pricing swap contracts and other financial products with multiple payout dates. In the special case of perfectly liquid markets or markets with proportional transaction costs, we recover well-known dual expressions in terms of martingale measures.     

具有交易费用和马氏调制的均值-方差组合选择

研究了均值-方差准则下,最优投资组合选择问题.投资者为了增加财富它可以在金融市场上投资.金融市场由一个无风险资产和n个带跳的风险资产组成,并假设金融市场具有马氏调制,买卖风险资产时,考虑交易费用.目标是,在终值财富的均值等于d的限制下,使终值财富的方差最小,即均值-方差组合选择问题.应用随机控制的理论解决该问题,获得了最优的投资策略和有效边界.     

Mean-variance portfolio rebalancing with transaction costs and funding changes

Investment portfolios should be rebalanced to take account of changing market conditions and changes in funding. Standard mean-variance (MV) portfolio selection methods are not appropriate for portfolio rebalancing, as the initial portfolio, change in funding and transaction costs are not considered. A quadratic mixed integer programming portfolio rebalancing model, which takes account of these factors is developed in this paper. The transaction costs in this portfolio rebalancing model are composed of fixed charges and variable costs, including the market impact costs associated with large market trades of individual securities, where these variable transaction costs are assumed to be non-linear functions of traded value. The use of this model is demonstrated and it is shown that when initial portfolio, funding changes and transaction costs are taken into account in portfolio construction and rebalancing, MV efficient portfolios that include risk-free lending do not have the structure expected from portfolio theory.     

A hybrid method for pricing European options based on multiple assets with transaction costs

The problem of pricing European options based on multiple assets with transaction costs is considered. These options include, for example, quality options and options on the minimum of two or more risky assets. The value of these options is the solution of a nonlinear parabolic partial differential equation subject to a final condition given by the payoff function associated with the option. A computationally efficient method to solve this final-value problem is proposed. This method is based on an asymptotic expansion of the required solution with respect to the parameters related to the transaction costs followed by the numerical solution of the linear partial differential equations obtained at each order in perturbation theory. The numerical solution of these linear problems involves an implicit finite-difference scheme for the parabolic equation and the use of the fast Fourier sine transform to solve the resulting elliptic problems. Numerical results obtained on test problems with the method proposed here are shown and discussed.     

基于排序预测的带交易费用在线投资组合策略

在线投资组合决策过程中频繁调整资产头寸会产生较多的交易费用。本文提出了一个综合考虑预期收益和交易费用的在线投资组合策略。通过预测资产的排序计算组合的预期收益,利用相对熵距离衡量交易费用,构造了一个极大化预期收益和极小化交易费用的优化模型,从而得到了一个在线投资组合更新策略。然后,从理论上证明了该策略具有BH泛证券性,即该策略与离线的最优购买并持有策略具有相同的渐近平均指数收益率。最后,采用中美股票市场实际数据,对该策略进行了数值分析。结果表明,该策略的表现优于已有的在线投资组合策略,且对模型的参数不敏感。     

CIR框架下的投资组合效用微分博弈

建立了Cox-Ingersoll—Ross随机利率下的关于两个投资者的投资组合效用微分博弈模型．市场利率具有CIR动力,博弈双方存在唯一的损益函数,损益函数取决于投资者的投资组合财富．一方选择动态投资组合策略以最大化损益函数,而另一方则最小化损益函数．运用随机控制理论,在一般的效用函数下得到了基于效用的博弈双方的最优策略．特别考虑了常数相对风险厌恶情形,获得了显示的最优投资组合策略和博弈值．最后给出了数值例子和仿真结果以说明本文的结论．     

Portfolio adjusting optimization under credibility measures

This paper discusses portfolio adjusting problems for an existing portfolio. The returns of risky assets are regarded as fuzzy variables and a class of credibilistic mean-variance adjusting models with transaction costs are proposed on the basis of credibility theory. Under the assumption that the returns of risky assets are triangular fuzzy variables, the optimization models are converted into crisp forms. Furthermore, we employ the sequential quadratic programming method to work out the optimal strategy. Numerical examples illustrate the effectiveness of the proposed models and the influence of the transaction costs in portfolio selection.