LQ理论在一类随机参数的跨国资产投资组合优化决策中的应用

考察在连续时间情形下,一类随机系数的跨国(主要研究两国之间)证券投资组合在均值-方差(M-V)优化准则下的最优投资策略(u*(t)),并进一步对该投资组合的有效边界进行研究,得出均值和方差之间的具体表达式.     

连续时间证券组合安全第一准则

马科维茨均值-方差分析是研究证券组合选择的一种基本方法,而Roy提出一种＂安全第一＂准则,该准则多出现在单阶段与多阶段证券组合选择的研究中.本文分别在完全信息与部分信息下,运用安全第一准则分别研究了连续时间证券组合选择问题,利用鞅方法与Malliavin分析得到投资者的最优投资策略.     

LQ理论在参数随机的证券投资组合套期保值中的应用

在连续时间情形、不考虑交易费用、市场无摩擦假设,以及套期保值准则等条件下,考察了参数随机的证券投资组合中加入未定权益类衍生品形成的最优动态投资策略(u*(t)),并给出了该投资组合的最优模型所对应的黎卡提(Riccati)方程的解的存在性证明.     

含交易费用的投资组合问题的新模型及其求解途径

本文提出了证券投资组合的一个新模型.该模型综合考虑了证券的收益率、证券分红和证券价格的关系,并将证券分红和证券价格作为系统的随机参数处理,建立了证券投资组合的随机规划模型.利用机会约束规划方法,我们研究了将所建立的随机规划模型转化为普通光滑优化问题求解的方法,得到了该类问题求解的有效途径.     

证券组合的模糊规划模型

通过结构元方法定义了一种模糊数排序准则,利用模糊约束将Markowitz投资组舍模型转化为模糊线性规划模型,并利用模糊数来描述证券的期望收益率和风险损失率,建立模糊数模糊证券投资组合模型.最后,利用定义的模糊数排序准则把模糊数规划问题转化为经典的线性规划问题,然后再对该模型进行求解,并通过算例阐述了该方法的有效性.     

时变β值证券组合投资决策模型研究

考虑证券收益的时变特性,将证券收益率看成随机序列,以β值证券组合投资决策模型为理论基础,提出了β值时变证券组合投资决策方法     

受约束的组合投资模型研究--最终财富效用优化

本文研究了证券投资者在某凸闭集下进行投资时使投资者的最终财富平均效用最大化的随机控制问题,获得了最优组合投资的等价性条件;证明了最优组合投资的存在性;在确定性 系数下,给出了最优投资反馈公式并讨论了一个简单的例子。     

与TSD准则一致的组合证券投资分析

基于预先给定的目标收益率,利用投资者对低于目标收益率的风险损失和高于目标收益率的风险报酬之间的权衡,给出了一些非对称风险度量模型,特别其中一种风险度量是低于参考点的方差和高于参考点的方差的加权和,它利用二阶上偏矩来修正二阶下偏矩,进一步建立了在该非对称风险度量下的组合投资优化模型,并证明了该模型在三阶随机占优的意义下是有效的.此外,还给出了其它3个模型与三阶随机占优准则是否一致的结论,并对所给出的几个组合证券投资模型的求解方法及其应用进行了分析.以上研究和分析为投资者在选择投资模型时避免盲目性、任意性提供了有益的决策参考.     

含不动产项目的保险公司再保险-投资策略

站在保险公司管理者的角度, 考虑存在不动产项目投资机会时保险公司的再保险--投资策略问题. 假定保险公司可以投资于不动产项目、风险证券和无风险证券, 并通过比例再保险控制风险, 目标是最小化保险公司破产概率并求得相应最佳策略, 包括: 不动产项目投资时机、 再保险比例以及投资于风险证券的金额. 运用混合随机控制-最优停时方法, 得到最优值函数及最佳策略的显式解. 结果表明, 当且仅当其盈余资金多于某一水平(称为投资阈值)时保险公司投资于不动产项目. 进一步的数值算例分析表明: (a)~不动产项目投资的阈值主要受项目收益率影响而与投资金额无明显关系, 收益率越高则投资阈值越低; (b)~市场环境较好(牛市)时项目的投资阈值降低; 反之, 当市场环境较差(熊市)时投资阈值提高.     

基于可信性安全准则的模糊动态投资组合模型

研究了模糊环境下的动态投资组合模型,将证券的收益率描述为模糊变量,提出了基于可信性测度的安全准则,可信性安全准则反映了投资者对灾难事件的容忍水平.建立了基于可信性安全准则的模糊动态投资组合模型,对建立的模型设计了基于模糊模拟的混合智能算法进行求解,并在Visual C++环境下,用C语言实现了对实例的求解,证明了混合智能算法的有效性和合理性.     

A mathematical model of pricing in a large system of cash bonds

The purpose of this paper is to give a mathematical model to generalize the classical approach of compound interest and to overcome the time structure problem of the interest rates. We introduce a suitable stochastic process called the ‘gauge’ process such that its product with the value of any security is assumed to be a martingale in an appropriate probability space. The framework of this model gives a stochastic actualization formula for the pricing of general securities with options and includes Black and Schole's formula without using arbitrage arguments. Emphasis has been placed on numerical calculation.     

Multiperiod Portfolio Optimization with Terminal Liability: Bounds for the Convex Case

This paper is concerned with an investor trading in multiple securities over many time periods in order to meet an outstanding liability at some future date. The investor is concerned with maximizing the expected profits from portfolio rebalancing under an initial wealth restriction to meet the future liabilities. We formulate the problem as a discrete-time stochastic optimization model and allow asset prices to have continuous probability distributions on compact domains. For the case of Markovian price uncertainty and convex terminal liability, we develop a simplicial approximation, under which bounds on the problem can be computed efficiently. Computations only require evaluating a dynamic programming recursion, which thus, allows its application to problems with a large number of trading periods. The bounds are tight in that they are exact in certain cases. Numerical results are given to demonstrate the computational efficiency of the procedure.     

EXISTENCE OF STOCHASTIC EQUILIBRIUM WITH INCOMPLETE FINANCIAL MARKETS

This paper analyzes the aritrage-tree security markets and the general equilibrium ex-istence problem for a stochastic economy with incomplete financial markets. Information structure is given by an event tree. This paper restricts attention to puraly financial securities. It isassume that trading takes place in the sequence of spot markets and futures markets for securi-ties payable in units of account. Unlimited short-selling in securities is allowed. Financial markets may be incomplete, some consumption streams may be impossible to obtain by any tradingstrategy. Securities may be individually precluded from trade at arbitrary states and dates. Thesecurity price process is arbitrage-free the dividend process if and only if there exists a stochaticstate price (present value) process : the present value of the security prices at every vertex isthe present value of their dividend and capital values over the set of immediate successors ; thecurrent value of each security at every vertex is the present value of its future dividend streamover all succeeding vertices. The existence of such an equilibrium is proved under the followingcondition: continuous, weakly convex, strictly monotone and complete preferences, strictlypositive endowmenta and dividends processes.     

一类投资组合优化问题的求解及实证分析

在证券投资组合优化的决策问题中,投资者通过选取不同的证券分散风险,为了使分散化的利益最大化,还须考虑证券组合的最佳规模以及交易成本。本文在给出求解这类问题的一种计算方法的基础上,进行实证分析。这里所用的方法以及结果,也适合于其他各种具有风险的投资决策问题。     

Stochastic regression and its application to hedging in finance

In this paper we investigate how to employ stochastic regression to hedge risks in finance, where the risk of a security is measured by its quadratic variation process. Mykland and Zhang used this technique to demonstrate how to reduce the risk of a given security by introducing another security. In this paper, we investigate how to further reduce the remaining unhedgable risk by adding more hedging securities. Some practical guidelines on how to choose those hedging securities in practice is also given. Jing’s research was partially supported by Hong Kong RGC (Grant Nos. HKUST6011/07P, HKUST6015/08P), and Zhang’s research was supported in part by National Natural Science Foundation of China (Grant No. 10771214)     

在线网络借贷投资决策模型及实证研究

P2P网络借贷作为电子商务在金融领域的延伸与应用,近年来得到广大学者的关注.但是目前的理论研究中,鲜有从投资者信息挖掘的角度进行投资决策分析.本文提出一个新颖的方法,即投资者构成分析方法,通过分析贷款的众多投资者信息遴选出最有价值的投资,辅助投资者进行投资决策.首先从投资者的历史投资收益率、风险偏好以及投资经验三个维度构建投资者档案(investor profile),进而基于投资者档案构建投资者构成分析模型,最后通过美国最大的在线网络借贷网站Prosper的数据,对本文提出的构想及模型进行了实证研究.实验结果表明本文提出的利用投资者构成分析的方法辅助投资者进行投资决策是可行的,文中构建的模型表现出良好的预测能力,能够有效地筛选出有价值的投资.     

重复n人随机合作对策的核心

以Su ijs等人(1995)引入的随机合作对策的模型为基础,建立了重复n人随机合作对策的理论,定义了重复n人随机合作对策的支付序列以及支付序列的优超关系,并由此给出了重复n人随机合作对策的核心、超可加性和凸性的定义,并讨论了该核心的一些特征和性质.     

Heston随机波动率市场中带VaR约束的最优投资策略

本文研究了Heston随机波动率市场下, 基于VaR约束下的动态最优投资组合问题。
假设Heston随机波动率市场由一个无风险资产和一个风险资产构成,投资者的目标为最大化其终端的期望效用。与此同时, 投资者将动态地评估其待选的投资组合的VaR风险,并将其控制在一个可接受的范围之内。本文在合理的假设下,使用动态规划的方法,来求解该问题的最优投资策略。在特定的参数范围内,利用数值方法计算出近似的最优投资策略和相应值函数, 并对结果进行了分析。     

Option Pricing in Illiquid Markets with Jumps

ABSTRACT

The classical linear Black–Scholes model for pricing derivative securities is a popular model in the financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying asset price dynamics following a geometric Brownian motion. The main purpose of this paper is to generalize the classical Black–Scholes model for pricing derivative securities by taking into account feedback effects due to an influence of a large trader on the underlying asset price dynamics exhibiting random jumps. The assumption that an investor can trade large amounts of assets without affecting the underlying asset price itself is usually not satisfied, especially in illiquid markets. We generalize the Frey–Stremme nonlinear option pricing model for the case the underlying asset follows a Lévy stochastic process with jumps. We derive and analyze a fully nonlinear parabolic partial-integro differential equation for the price of the option contract. We propose a semi-implicit numerical discretization scheme and perform various numerical experiments showing the influence of a large trader and intensity of jumps on the option price.     

Increasing risk aversion and life-cycle investing

Mathematics and Financial Economics - We derive the optimal portfolio for an investor with increasing relative risk aversion in a complete continuous-time securities market. The IRRA assumption...