最优变现策略及最优变现时间

研究了变现时间内生时,投资者的最优变现策略和最优变现时间问题,市场价格的永久冲击和瞬时冲击均为变现速度的线性函数,并且变现速度是一带孤立点的闭集合,利用最优控制理论中的极大值原理,得到了问题的解析解,研究结论表明,最优变现策略和变现时间由市场条件、股票的波动性、流动性、头寸规模和投资者的风险偏好共同决定;永久冲击只影响变现的收益,与最优变现策略和时间无关。     

非线性价格冲击函数下的最优变现策略

研究了在非瓦尔拉斯市场中,当市场的价格冲击函数为变现速度的非线性函数时,投资者的最优变现策略和最优变现时间问题。利用控制理论中的极大值原理,获得了作为控制变量的最优变现策略,同时也得到了最优变现时间。建立的市场模型在价格形成、交易制度方面接近现实经济中的市场。研究结论表明,变现时间内生时,在机构投资者应用最优变现策略情况下,没有出清手中所有头寸前,机构投资者的变现速度必不为零。     

开放式基金流动性风险的最优控制

在证券价格服从离散时间算术布朗运动的假设下，得到资产流动性风险最优控制策略，并对该策略进行有关参数的敏感性分析。研究结果表明，流动性系数较大时，最优控制策略接近于线性策略；流动性系数较小时，资产管理者会迅速将资产头寸降至理想水平，并在大部分时间内保持这种状态，直到变现期末达到资产目标头寸。最优策略对管理者的风险厌恶程度、资产波动率和流动性系数较为敏感，而对证券超额收益率敏感程度较低。     

Heston模型中具有保费退回的确定缴费型养老金均衡投资策略

本文基于均方差准则研究了Heston模型中确定缴费型养老金(defined contribution,DC)计划的最优投资策略.假定养老金计划可投资于一种无风险资产和一种风险资产(股票),风险资产的价格服从收益率和波动率均为随机的Heston模型.此外,为了保护在基金积累阶段意外死亡的投保人的利益,假定保费可退回(给其继承人).本文在博弈论框架下给出了相应的HJB方程系统,并通过求解相应的HJB方程系统,得到了最优"时间一致"均衡投资策略以及均衡有效前沿的解析式.据我们所知,这是首次在具有保费退回的情形中研究Heston模型中DC计划的均方差均衡投资问题.文章最后分析了最优均衡投资策略和有效前沿的相关性质.     

基于Agent的我国股票市场卖空机制仿真研究

针对我国股市现有的卖空约束缺陷,用复杂适应系统的思想和方法分析股市的复杂性,运用Swarm平台,构建基于Agent的直接计算机模型。设定模型由“交易事件”驱动,给定Agent理性和非理性的行为规则,让Agent通过对有关数据分析后建立有偏预期或无偏预期的交易策略,从而导致资产价格和交易量的变化,以此分析引入卖空机制对股市的影响。仿真模拟表明,卖空机制可以把价格风险降低,增加市场的流动性,对改变股市的资产结构有积极影响,成为投资者和市场规避风险的工具。     

随机金融市场环境下的最优再保险–投资策略

为了对冲保险风险,保险公司可以向再保险公司购买比例再保险;同时,为了保值增值,保险公司将其财富投资于金融市场.假设盈余过程由带漂移的布朗运动所驱动,利率满足仿射利率模型,股票波动率满足Heston随机波动率模型.应用随机最优控制和HJB方程方法得到了指数效用下最优再保险–投资策略的显式解.给出数值算例并分析了模型参数对最优再保险策略和最优投资策略的影响.研究结果表明:最优再保险策略不仅依赖于保险市场参数,而且依赖于金融市场参数;随机利率与随机波动率模型下的最优再保险–投资策略与利率动态密切相关,而与波动率动态无关;再保险行为对投资于股票的数量没有影响,而对投资于零息票债券的数量产生较大的影响.     

基于鲁棒控制的期权套期保值策略

在标的资产价格服从带有随机方差几何布朗运动的非完全市场假设条件下,应用随机微分对策方法,研究与标的资产有关的欧式期权的动态套期保值策略问题。建立了最优动态套期保值策略的随机微分对策数学模型,给出了基于鲁棒控制的均方复制误差最小的自融资动态套期保值策略。当方差为时间的确定性函数时,最优动态套期保值策略与用Black-Scholes套期比表示的delta套期保值策略是一致的。     

多阶段均值–方差资产负债管理的随机控制

资产负债管理研究如何合理分配资产以到达最小化风险同时确保期望剩余财富(财富减去负债)达到一定水平.本文在均值–方差投资组合理论的框架下研究两类资产负债管理模型, 包括带有跨期均值–方差投资目标和带有非破产约束的模型. 由于在动态规划意义下, 方差不具有可分性质, 传统的随机最优控制方法难以直接应用. 如采用处理动态均值–方差优化问题的嵌入法来解决以上问题会带来计算上的困难. 本文借鉴平均场控制的思想对以上两类问题加以研究. 本文假设了非常宽泛的市场模型: 所有的资产都是风险资产; 债务和风险资产之间存在相关性. 在此市场假设模型下, 本文给出了最优投资策略(控制率)的解析表达式和均值–方差有效前沿的表达形式. 本研究成果为投资者提供了新的投资策略, 可应用于更复杂的资产负债管理中.     

随机利率与随机波动率环境下的DC型养老金计划

为实现养老金的保值增值,基金管理人将养老金投资于金融市场.假设金融市场包含一种无风险资产、一种股票和一种零息票债券,其中,利率期限结构满足随机仿射利率模型,而股票价格波动率满足Heston随机波动率模型.基金管理人希望寻找一种最优投资组合以最大化其终端财富的期望效用.假设基金管理人对风险的偏好满足幂效用或指数效用,运用随机动态规划原理和变量替换方法,得到幂效用和指数效用下最优投资策略的显式解.最后,通过数值算例分析主要模型参数对最优投资策略的影响.研究结果表明,利率风险、股市波动风险以及缴费率都对缴费确定(DC)型养老金的投资决策产生较大的影响.     

多阶段均值-方差资产负债管理的随机控制（英文）

资产负债管理研究如何合理分配资产以到达最小化风险同时确保期望剩余财富(财富减去负债)达到一定水平.本文在均值-方差投资组合理论的框架下研究两类资产负债管理模型,包括带有跨期均值-方差投资目标和带有非破产约束的模型.由于在动态规划意义下,方差不具有可分性质,传统的随机最优控制方法难以直接应用.如采用处理动态均值-方差优化问题的嵌入法来解决以上问题会带来计算上的困难.本文借鉴平均场控制的思想对以上两类问题加以研究.本文假设了非常宽泛的市场模型:所有的资产都是风险资产;债务和风险资产之间存在相关性.在此市场假设模型下,本文给出了最优投资策略(控制率)的解析表达式和均值-方差有效前沿的表达形式.本研究成果为投资者提供了新的投资策略,可应用于更复杂的资产负债管理中.     

Research on the Effects of Institutional Liquidation Strategies on the Market Based on Multi-agent Model

Based on the multi-agent model, an artificial stock market with four types of traders is constructed. On this basis, this paper focuses on comparing the effects of liquidation behavior on market liquidity, volatility, price discovery efficiency and long memory of absolute returns when the institutional trader adopts equal-order strategy, Volume Weighted Average Price (VWAP) strategy and Implementation Shortfall (IS) strategy respectively. The results show the following: (1) the artificial stock market based on multi-agent model can reproduce the stylized facts of real stock market well; (2) among these three algorithmic trading strategies, IS strategy causes the longest liquidation time and the lowest liquidation cost; (3) the liquidation behavior of institutional trader will significantly reduce market liquidity, price discovery efficiency and long memory of absolute returns, and increase market volatility; (4) in comparison, IS strategy has the least impact on market liquidity, volatility and price discovery efficiency, while VWAP strategy has the least impact on long memory of absolute returns.

     

Optimal allocation–consumption problem for a portfolio with an illiquid asset

During financial crises investors manage portfolios with low liquidity, where the paper-value of an asset differs from the price proposed by the buyer. We consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. We work in the Merton's optimal consumption framework with continuous time. The liquid part of the investment is described by a standard Black–Scholes market. The illiquid asset is sold at a random moment with prescribed distribution and generates additional liquid wealth dependent on its paper-value. The investor has a hyperbolic absolute risk aversion also denoted as HARA-type utility function, in particular, the logarithmic utility function as a limit case. We study two different distributions of the liquidation time of the illiquid asset – a classical exponential distribution and a more practically relevant Weibull distribution. Under certain conditions we show the smoothness of the viscosity solution and obtain closed formulae relevant for numerics.     

Trading Volume and Price Distortion: An Agent-Based Model with Heterogenous Knowledge of Fundamentals

This paper investigates whether trading volume and price distortion can be explained by the investor’s bounded rationality. Assuming that agents are bounded by their information access and processing, what are the consequences on market dynamics? We expose the result of simulations in an ABM that considers the liquidity as an endogenous characteristic of the market and allows to design investors as bounded rational. In a call auction market, where two risky assets are exchanged, traders are defined as a mix between fundamentalist and trend-follower outlook. Each one differs as to behaviour, order-placement strategy, mood, knowledge, risk-aversion and investment horizon. We place agents in a context of evolving fundamental values and order placement strategy; they perceive the fundamental but they also have some heterogeneous belief perseverance; and they adapt their orders to the market depth so as to maximise their execution probability and their profit. By adding bounded rationality in their information processing, we show that (1) usual features as trend-follower outlook and heterogeneous investment horizon are important features to generate excess volatility of asset prices and market inefficiency; (2) the learning fundamental value stabilises the market price and the trading volume; (3) the order-placement strategy increases trading volume, but reduces market efficiency and stability; (4) the agent’s mood prevents illiquid market and weakly increases the market volatility as classical noise trader agents; (5) the impatience to sell of traders is always present in the market: the market sell orders are always more numerous than the market buy orders.     

A fuzzy modeling for fuzzy portfolio optimization

Conventional portfolio optimization models have an assumption that the future condition of stock market can be accurately predicted by historical data. However, no matter how accurate the past data is, this premise will not exist in the financial market due to the high volatility of market environment. This paper discusses the fuzzy portfolio optimization problem where the asset returns are represented by fuzzy data. A mean-absolute deviation risk function model and Zadeh’s extension principle are utilized for the solution method of portfolio optimization problem with fuzzy returns. Since the parameters are fuzzy numbers, the gain of return is a fuzzy number as well. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the return of the portfolio optimization problem. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a pair of ordinary one-level linear programs so they can be manipulated. It is found that the calculated results conform to an essential idea in finance and economics that the greater the amount of risk that an investor is willing to take on, the greater the potential return. An example, which utilizes the data from Taiwan stock exchange corporation, illustrates the whole idea on fuzzy portfolio optimization problem.     

Effective options trading strategies based on volatility forecasting recruiting investor sentiment

This study investigates an algorithm for an effective option trading strategy based on superior volatility forecasts using actual option price data for the Taiwan stock market. The forecast evaluation supports the significant incremental explanatory power of investor sentiment in the fitting and forecasting of future volatility in relation to its adversarial multiple-factor model, especially the market turnover and volatility index which are referred to as the investors’ mood gauge and proxy for overreaction. After taking into consideration the margin-based transaction cost, the simulated trading indicates that a long or short straddle 15 days before the options’ final settlement day based on the 60-day in-sample-period volatility forecasting recruiting market turnover achieves the best average monthly return of 15.84%. This study bridges the gap between option trading, market volatility, and the signal of the investors’ overreaction through the simulation of the option trading strategy. The trading algorithm based on the volatility forecasting recruiting investor sentiment could be further applied in electronic trading and other artificial intelligence decision support systems.