基于流动性约束和价格趋势的最优交易策略

股票市场中当交易规模较大时,投资者不仅要预判未来的股票价格趋势从而降低风险成本,也要考虑大额交易指令对市场冲击的成本.在投资者预判股票未来价格趋势的同时,考虑交易量的线性价格冲击,建立一个控制最小交易成本的策略模型,采用随机动态规划方法得出总体执行成本最小的交易策略解析解,进一步利用数值算例对最优交易策略进行了比较静态分析.     

基于动态交易量预测的VWAP算法交易卖出策略

传统的VWAP交易策略通过预测区间交易量分布进行拆单交易,对于交易量区间分布的预测是基于区间成交量占总成交量比例进行的,这一预测方法没有考虑股票价格变动因素。因此,本文首先通过时间序列因素分解方法进行区间交易量分布预测,进而根据股票价格变化对区间交易量分布进行动态调整,并构建了基于动态区间交易量分布的股票卖出策略,最后通过实证检验了本文给出的动态区间交易量分布预测的有效性和交易策略的有效性。数值结果表明,本文所给动态区间交易量分布预测方法比传统VWAP方法预测结果更加接近于实际的交易量分布,且本文所给交易策略与传统VWAP交易策略相比,具有更大的收益。     

基于跳扩散过程的可转换债券的定价

本文标的股票的方程采用跳扩散方程,首先规定一个跳跃的涨跌区间,这样就可以很快的找出跳跃点,我们根据跳跃点将股价聚类,然后把各个类看成是总体中抽取出来的一个样本,我们就可以估计出跳扩散方程中的所有参数.由于我们的标的股票的方程是含跳过程,因此无法找出完全保值的自融资策略,但我们可以根据风险最小化的原理给出可转换债券的价格,最后运用Monte Carlo模拟计算出了南京水运转债在0时刻的价格。     

部分信息下带有保费返还条款的DC养老金时间一致性投资策略

本文研究了部分信息下带有保费返还条款的DC养老金的时间一致性投资策略.假设养老金管理者只拥有股票的部分信息,即只能观测到股票的价格,而不能观测到股票的收益率.养老金带有保费返还条款,在基金累积期死亡的参与者可以获得前期缴纳的所有保费.此外,本文还考虑了通胀风险以及随机工资.首先,利用卡尔曼滤波理论,将部分信息情形下的最优投资组合问题转化为一个完全信息情形下的问题.然后,通过求解一个扩展的HJB方程,得到时间一致性投资策略和最优值函数,并给出了均值–方差有效前沿的参数表达式.最后,用蒙特卡洛方法进行数值模拟,分析了部分信息和保费返还条款对股票投资比例和有效前沿的影响,并给出了相应的经济学解释.     

有交易费时的欧式期权定价

本文考虑存款与借款利率不同且对股票的交易有交易费要求时的欧式期权定价问题。我们假定投资者的投资目的是使自己的期望效用最大化。对于市场给出的期权价格,投资者将选择最优的资产组合。在投资者的这种行为下,可以认为市场是投资者的对手,而期权的市场价格将会这样给出：投资者在这个价格下,他的最大期望效用将达到最小。本文在假定投资者的效用函数为风险中性时,给出了有交易费时欧式期权价格的显式表达式。     

损耗性物品信用交易下的斯坦博格库存模型

目前众多的信用交易模型是在供应商给定的信用交易期限条件下,零售商确定最优订购数量或订购周期,而很少考虑供应商信用交易策略的制定问题。本文针对损耗性物品,在最终需求为价格的线性函数条件下,利用斯坦博格博弈模型给出了信用交易下供应商信用交易策略的制定和零售商的最优订购决策,最后通过算例对模型进行了验证。     

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%。     

基于GRA-CS-BP算法的期货价格预测

针对在采用BP神经网络进行期货价格预测时,存在的模型结构复杂,易陷入局部极小值,模型无法收敛问题.考虑从网络结构和网络参数两个方面对BP网络模型进行优化,由此提出基于GRA-CS-BP算法的期货价格预测方法.首先用灰色关联度分析法进行输入变量筛选,找出和预测价格关联度大的重要因素作为网络输入,简化网络模型整体结构.然后采用布谷鸟算法对网络权阈值参数进行优化,将经过选择优化后建立的BP神经网络模型用于期货价格预测.仿真结果表明,新模型不仅具有更高的预测精度,同时其运行的稳定性也要好于单纯BP神经网络模型,为期货价格预测提出了一种新的方法.     

复合Poisson模型带投资-借贷利率和固定交易费用的最优分红策略

本文研究了复合Poisson模型带投资-借贷利率和固定交易费用的最优分红问题。通过控制分红时刻和分红量，最大化直到绝对破产时刻的累积期望折现分红。由于考虑固定交易费用，问题为一个随机脉冲控制问题。首先，本文给出了一个策略是平稳马氏策略的充分必要条件。借助于测度值生成元理论得到测度值动态规划方程(简称测度值DPE),并且在没有任何附加条件下证明了验证定理。通过Lebesgue分解，本文讨论了测度值DPE和拟变分不等式(简称QVI)之间的关系，证明了最优分红策略为具有波段结构的平稳马氏策略。最后，本文给出了求解n-波段策略和相应值函数的算法。当索赔额服从指数分布时，得到了值函数的显示解和最优分红策略。     

电力市场中合同电量与竞争电量交易比例的研究

在单边开放的区域电力市场中,合理的合同电量与竞争电量交易比例是保证电力市场有效运行的一个重要环节。竞争电量所占的比例将主要取决于当前发电公司的市场行为。首先使用BP神经网络对电力需求弹性系数进行了预测,然后以长期电力市场均衡为目标函数,考虑贵州电网发电机组的可用容量与负荷预测的误差,以及贵州输电线路的可靠性诸因素,推导出合同电量与竞争电量交易比例,经过与南方区域电力市场目前运营规则规定的交易比例比较,该比例是合理的,可以规避电力市场价格波动等带来的风险。     

Fuzzy adaptive decision-making for boundedly rational traders in speculative stock markets

The development of new models that would enhance predictability for time series with dynamic time-varying, nonlinear features is a major challenge for speculators. Boundedly rational investors called “chartists” use advanced heuristics and rules-of-thumb to make profit by trading, or even hedge against potential market risks. This paper introduces a hybrid neurofuzzy system for decision-making and trading under uncertainty. The efficiency of a technical trading strategy based on the neurofuzzy model is investigated, in order to predict the direction of the market for 10 of the most prominent stock indices of U.S.A, Europe and Southeast Asia. It is demonstrated via an extensive empirical analysis that the neurofuzzy model allows technical analysts to earn significantly higher returns by providing valid information for a potential turning point on the next trading day. The total profit of the proposed neurofuzzy model, including transaction costs, is consistently superior to a recurrent neural network and a Buy & Hold strategy for all indices, particularly for the highly speculative, emerging Southeast Asian markets. Optimal prediction is based on the dynamic update and adaptive calibration of the heuristic fuzzy learning rules, which reflect the psychological and behavioral patterns of the traders.     

An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions

This paper is concerned with an optimal strategy for simultaneously trading of a pair of stocks. The idea of pairs trading is to monitor their price movements and compare their relative strength over time. A pairs trade is triggered by their prices divergence and consists of a pair of positions to short the strong stock and to long the weak one. Such a strategy bets on the reversal of their price strengths. From the viewpoint of technical tractability, typical pairs-trading models usually assume a difference of the stock prices satisfies a mean-reversion equation. In this paper, we consider the optimal pairs-trading problem by allowing the stock prices to follow general geometric Brownian motions. The objective is to trade the pairs over time to maximize an overall return with a fixed commission cost for each transaction. The optimal policy is characterized by threshold curves obtained by solving the associated HJB equations. Numerical examples are included to demonstrate the dependence of our trading rules on various parameters and to illustrate how to implement the results in practice.     

一般均衡下基于产品市场和资本市场的单名CDS定价

次贷危机呼吁新的信用衍生品定价模型, 因此为存在产品市场和资本市场的经济结构建立一般均衡的单名CDS定价模型, 使用最优化求解一般均衡下的商品价格和CDS价格. 可以发现一般均衡的CDS定价具有资本市场和产品市场的因素, 这表示CDS的价格不再是由单纯的资本市场因素决定的, 而是由无风险利率、资本产出弹性、违约率、回收率同时决定的. 通过数量约束用模拟的方式研究多个均衡的动态变化, 发现违约风险的增加使得价格剧烈波动且市场交易萎缩. 在为以中国工商银行为参考资产的CDS定价过程中, 发现各种因素在不同的时期都可能成为定价的主要影响因素. 可以发现, 次贷危机的定价体系存在着信用调整问题和定价与实体经济脱节的问题. 可以认为, 一般均衡下基于产品市场和资本市场的单名CDS定价可以囊括多个市场的交叉影响, 为衍生品定价提供一个新的方向.     

Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies

ABSTRACT

We compare optimal liquidation policies in continuous time in the presence of trading impact using numerical solutions of Hamilton–Jacobi–Bellman (HJB) partial differential equations (PDEs). In particular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent (pre-commitment) mean-variance strategy. We show that the two different risk measures lead to very different strategies and liquidation profiles. In terms of the optimal trading velocities, the mean-quadratic-variation strategy is much less sensitive to changes in asset price and varies more smoothly. In terms of the liquidation profiles, the mean-variance strategy is much more variable, although the mean liquidation profiles for the two strategies are surprisingly similar. On a numerical note, we show that using an interpolation scheme along a parametric curve in conjunction with the semi-Lagrangian method results in significantly better accuracy than standard axis-aligned linear interpolation. We also demonstrate how a scaled computational grid can improve solution accuracy.     

基于M-LSTM的股票指数日内交易量分布预测研究

针对现有预测建模方法难以高效提取日内交易量分布复杂变化规律,影响VWAP策略执行效果的问题,本文提出一种MEMD分解下基于LSTM-Attention的股市指数日内交易量分布预测方法M-LSTM。首先,运用MEMD方法将区间多维交易量时序同步分解为若干个独立的本征模态函数(IMF);其次,对各维度分解中高频IMF进行去噪与重构,构建基于LSTM-Attention神经网络的日内交易量分布预测模型,并深入分析股票指数不同走势阶段下模型预测的有效性;最后,分别采用M-LSTM、ARIMA以及SVR等主流方法,对上证指数等四个代表性指数的日内交易量分布进行预测。实验结果表明:M-LSTM预测误差更小,是一种更有效的股票指数日内交易量分布预测方法。     

Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions

We study optimal liquidation of a trading position (so-called block order or meta-order) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the unaffected asset price while simultaneously ruling out short sales. In this setting the liquidation time horizon becomes a stopping time determined endogenously, as part of the optimal strategy. We find that the optimal liquidation strategy is consistent with the square-root law which states that the average price impact per share is proportional to the square root of the size of the meta-order (Bershova & Rakhlin,2013; Farmer et?al., 2013; Donier et?al., 2015; Tóth (2016).Mathematically, the Hamilton–Jacobi–Bellman equation of our optimization leads to a severely singular and numerically unstable ordinary differential equation initial value problem. We provide careful analysis of related singular mixed boundary value problems and devise a numerically stable computation strategy by re-introducing time dimension into an otherwise time-homogeneous task.     

基于EEMD-Elman-Adaboost的中美股票价格预测研究

针对股票价格序列高度非正态、非线性、非平稳等复杂特征,文章以Elman神经网络为基础,引入集合经验模态分解(EEMD)与Adaboost算法,对中美股票的日收盘价进行预测。首先,利用EEMD算法将样本分解为多个本征模函数分量和1个残差分量。其次,用Adaboost算法优化Elman神经网络,对各个分量进行预测。最后,将各分量预测结果进行求和,作为最终预测结果。研究结果表明:EEMD-Elman-Adaboost模型对中美股票价格预测的均方根误差、平均相对误差、平均绝对误差均比现有的BP、Elman、EMD-Elman、EEMD-Elman模型小,新组合模型融合了EEMD、Elman神经网络、Adaboost算法的优点,具有更强的泛化能力和跟随能力。     

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.