金融决策问题的在线策略及其竞争分析

发布时间：2019-05-23 05:41

【摘要】：理论计算机学科兴起的在线学习算法的特点是不对未来输入序列作任何统计假设和仅根据已获得信息进行决策，这为许多具有在线特点的金融决策问题的研究提供了新思路和方法。该文首先论述了设备资产租赁、单一风险资产投资和多种风险资产投资等金融决策问题的研究背景和意义；回顾了决策理论的起源与发展并论述了国内外研究现状。在此基础上，结合实际情况，应用传统竞争比分析方法进一步研究了设备资产在线租赁策略和风险策略。探讨了单一风险资产的在线投资策略，分别给出了基于风险厌恶型的保守策略和基于预期的风险策略。提出了基于线性学习函数的多种风险资产在线投资策略并分析了其竞争性能；将弱集成在线学习算法应用到多种风险资产在线投资，给出了具体在线决策策略。设备资产在线租赁、单一风险资产在线投资和多种风险资产在线投资的研究方法既有区别又有明显的关联。它们的输入都具有在线性，都根据已获得的历史数据进行决策，都需要选择一个标准来衡量所给在线策略的竞争性能。设备资产在线租赁是最简单最基本的风险决策问题之一，可将它的研究方法推广应用到单一风险资产在线投资和多种风险资产在线投资，，而单一风险资产在线投资又是多种风险资产在线投资的一种特例。具有创新性的研究成果主要包括以下几个方面： 1.研究了受市场供求关系变化、自由市场灵活性和间隔使用设备等因素影响的在线租赁问题，建立了对应的在线租赁模型，用竞争分析方法得到了相应的在线租赁策略及其竞争性能分析。设备的购买价格和租赁费用往往随着需求量变动而发生改变；同时随着科技的发展，设备的品牌层出不尽；并且市场利率会对阶段性使用设备的在线策略产生影响。基于此，本文研究了设备价格离散可变的在线租赁策略及其竞争性能，探讨了多种设备获得方式的可折旧设备租赁的在线随机选择策略，给出了受市场利率影响的两阶段在线租赁策略的竞争性能分析。 2.针对大型设备的可折旧性和二手市场的存在性，建立了可折旧设备在线租赁模型，得到了它的确定性策略、随机性策略和基于预期的风险策略。关于设备租赁问题的大多数研究都是建立在设备一旦购买便永久可以使用的基础上，而并没有对可折旧设备在线租赁问题的竞争策略进行系统的研究，本文在可折旧设备在线租赁模型建立的基础上，首先给出了它的确定性策略和随机性策略，进一步给出了它在确定性预期下的风险策略和在概率预期下的风险策略，最后并将确定性预期下的风险策略运用到了两阶段在线设备更新问题中。结果表明折旧的引入使得确定性策略和随机性策略的竞争性能有所提高，市场利率的引入使得最优确定性竞争比有所减少，却使得最优随机性竞争比有所增大；风险策略的最优约束竞争比减少幅度与风险容忍度成正比；结果也表明了概率预期下的风险策略扩展了确定性预期下的风险策略。 3.研究了风险资产收益率线性变动和对数变动情形下的单一风险资产投资问题，建立了阶段性预期下单一风险资产在线投资的风险补偿模型，分别得到了单一风险资产在线投资的保守策略和风险策略。实际风险资产收益率波动的形式多样，从风险厌恶角度本文分别给出了每期风险资产收益率变化服从线性波动和对数波动的保守投资策略。数值算例说明了基于风险厌恶型的单一风险资产在线投资策略更适合于波动平稳的风险资产收益率序列。已有的风险策略是基于风险资产收益率变化点的预期，本文给出了阶段性预期下单一风险资产投资的风险策略及其竞争性能分析，数值算例同时也表明了阶段性预期下最优约束竞争比的平均改善幅度与投资者的风险容忍度密切相关并且成正比。 4.研究了多种风险资产的在线投资问题，建立了基于线性学习函数的在线投资组合策略，得到了一类泛证券投资组合策略；并建立了基于弱集成学习算法的多种风险资产在线投资模型，得到了竞争性能较好的在线投资策略。提出了基于线性学习函数的多种风险资产在线投资策略，其中线性函数的系数是一个与风险资产收益率有关的区间中点。用相对熵函数定义两个投资组合向量之间的距离，证明了所给出的在线投资组合是泛证券投资组合。当线性系数取值于区间的任意一点时，得到了一类泛证券投资组合。探讨了弱集成算法在多种风险资产在线投资组合选择中的应用。首先将弱集成学习算法应用到投资于单个风险资产的专家策略，得到了多种风险资产在线投资策略WAAS。考虑到泛证券投资组合策略是相对于最优定常再调整策略而言的，进一步将弱集成算法应用到定常再调整策略，得到了多种风险资产在线投资策略WAAC。理论和数值算例都说明了WAAS策略的收益与表现最好的风险资产的收益相当；WAAC策略的收益与最优定常再调整策略的收益相当。
[Abstract]:The feature of the online learning algorithm of the theory computer science is not to make any statistical assumptions on the future input sequence and to make decision only according to the obtained information, which provides a new thought and method for many research on the financial decision-making problem with on-line characteristics. This paper first discusses the research background and significance of the financial decision-making problems such as equipment asset lease, single-risk asset investment and multiple risk assets investment, and reviews the origin and development of the decision-making theory and discusses the domestic and foreign research status. On this basis, according to the actual situation, the online lease strategy and the risk strategy of the equipment assets are further studied by using the traditional competitive ratio analysis method. The online investment strategy of single-risk assets is discussed, and the conservative strategy based on risk aversion and the expected risk strategy are given. The online investment strategy of multiple risk assets based on linear learning function is put forward and its competitive performance is analyzed. The online learning algorithm of weak integration is applied to the on-line investment of multiple risk assets, and the specific online decision-making strategy is given. The research methods of on-line lease of equipment assets, on-line investment of single-risk assets and on-line investment of multiple risk assets have the distinct and obvious correlation. Their inputs are both linear and based on the historical data that have been obtained, and a criterion is required to measure the competitive performance of the on-line strategy. The on-line leasing of equipment assets is one of the most basic and most basic risk decision-making problems. It can be applied to on-line investment of single-risk assets and on-line investment of multiple risk assets, while on-line investment of single-risk assets is a special case of on-line investment of multiple risk assets. The innovative research results mainly include the following aspects: 1. The online lease problem, which is affected by market supply and demand relationship change, free market flexibility and space usage equipment, is studied, and the corresponding online lease is established In this paper, the competitive analysis method is used to obtain the corresponding online lease strategy and its competitive performance. Analysis. The purchase price and the lease cost of the equipment tend to change with the change of demand; with the development of science and technology, the brand of the equipment is inexhaustible; and the market interest rate will be an on-line policy of the stage-use equipment. On the basis of this, this paper studies the online lease strategy and its competitive performance of the discrete variable of the equipment price, and discusses the online random selection strategy of the depreciation equipment lease of various equipment acquisition modes, and gives the two-stage online lease strategy influenced by the market interest rate. 2. Based on the depreciation and the existence of the second-hand market of the large-scale equipment, the on-line lease model of the depreciable equipment is established, and its deterministic strategy, the random strategy and the base are obtained. Most of the studies on equipment rental problems are based on the permanent availability of the equipment once they are purchased, and there is no systematic study of the competitive strategy for the on-line leasing of the depreciable equipment, in which the depreciation equipment is On the basis of the establishment of the line lease model, the deterministic strategy and the stochastic strategy are given, and the risk strategy and the risk strategy under the expectation of certainty are further given. Finally, the risk strategy of the deterministic expectation is applied to the two. The results show that the introduction of depreciation causes the competitive performance of the deterministic strategy and the stochastic strategy to be improved, and the introduction of the market interest rate makes the optimal deterministic competition ratio decrease, but the most The superior and random competition ratio is increased; the optimal constraint competition ratio of the risk strategy is directly proportional to the risk tolerance; the result also shows that the risk strategy under the expectation of the probability is expanded 3. The risk compensation model of single-risk assets on-line investment in the case of linear fluctuation and log-change of risk assets is studied, and the risk compensation model of single-risk assets on-line investment is established, and the single-risk assets are obtained respectively. The conservative strategy and the risk strategy of on-line investment. A conservative investment strategy based on the linear fluctuation and the log fluctuation is given. The numerical example shows that the on-line investment strategy of a single-risk assets based on the risk-aversion type is more The existing risk strategy is based on the expectation of the change point of the rate of return of the risk assets, and the single risk is given in this paper. The risk strategy of the asset investment and its competitive performance analysis, the numerical example also shows the average improvement amplitude and the investment of the optimal constrained competition ratio at the same time. 4. The on-line investment problem of multiple risk assets is studied, and an online portfolio strategy based on linear learning function is established. On-line investment of multiple risk assets of weak integrated learning algorithm In this paper, the on-line investment strategy with good competitive performance is obtained. The online investment strategy of multiple risk assets based on the linear learning function is put forward, in which the linear learning function is linear. The coefficient of the function is the midpoint of the interval that is related to the rate of return of the risk assets. The distance between the two portfolio vectors is defined by the relative entropy function It is proved that the combination of on-line investment and on-line investment is a combination of pan-securities investment. When the linear coefficient is taken, At any point in the interval, a generic portfolio of portfolio investment has been obtained. The application of the integration algorithm in the selection of the on-line portfolio selection of multiple risk assets. Firstly, the weak integrated learning algorithm is applied to the individual risk assets. In this paper, a wide range of risk assets on-line investment strategy (WAAS) is obtained. Considering that the pan-securities investment portfolio strategy is relative to the optimal time-invariant re-adjustment strategy, the weak integration algorithm is further applied to the steady re-adjustment In this paper, a wide range of risk assets online investment strategies (WAAC) are obtained. The theoretical and numerical examples show that the benefit of the WAAS strategy is equivalent to that of the best risk assets; and W
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F830;F224

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