以可存品与非可存品为消费对象的最优投资消费决策

传统的投资消费决策问题考虑的消费对象局限于单一的非可存品或者单一的可存品 .而且假定银行的贷款利率等于存款利率 .本文假定银行的贷款利率大于存款利率 ,并且投资者的消费对象为包含可存品与非可存品的组合 .可存品的价格假设服从几何布朗运动 ,它的折旧率假定为一个常值 .应用随机控制方法 ,得到等弹性效用函数情形下的最优投资消费策略的显式表达     

存贷利率不等下具有随机跳跃收入的消费与投资策略

研究贷款利率大于存款利率下具有随机跳跃收入的最优策略,拓展了Merton模型.给出了财富预算方程,运用动态规划原理及随机分析导出该问题的HJB方程,并由此得到一般情形下抽象形式的解.在一类特殊HARA情形下讨论了具有显式反馈形式的最优消费和投资策略.     

基于易腐品和不可分割耐用品的最优消费投资与寿险购买策略

随着经济的发展和人民生活水平的提高,投资者的投资组合不再局限于证券市场投资.通过将寿险购买引入投资者的投资组合并划分消费品为易腐品或不可分割耐用品,研究投资者的最优消费投资与寿险购买策略.投资者的投资目标为期望效用最大化.运用动态规划原理得到哈密尔顿-雅可比-贝尔曼方程,最终得到最优策略满足的方程,并讨论方程存在正根的条件.最后通过数值分析方法,验证模型结论与实际现实情况的一致性.     

跳跃扩散股价的最优投资组合选择

假定股票价格服从跳跃扩散过程.在传统均值-方差组合投资模型基础上,最大化最终收益的期望及最小化最终财富的方差.引进一个随机线性二次最优控制问题作为原问题的近似问题.证明了一个状态为跳跃扩散过程的一般最优控制问题的验证性定理.应用验证性定理求解HJB(Hamilton-Jacobi-Bellman)方程得到了原问题的最优策略.最后还给出了原问题有效前沿的表达式.     

一类国际证券投资组合和消费选择的最优控制问题

首先运用经典动态规划方法,研究股票付息下国际证券市场中一类最优证券投资组合和消费选择问题,并利用投资学理论对投资者只投资两种证券情形的最优组合给出经济分析和解释.然后,运用非常简单和直接的方法对两种典型的效用函数给出最优解的显式形式,求解的技巧来自解决线性二次最优控制问题的配平方法.最后,给出一些数值计算例子来展示各模型参数对最优选择的影响.     

复杂最优消费组合问题的数值逼近解算法

针对由现有理论和方法求不到显式解的复杂最优消费组合问题,提出基于参数待定法以及遗传算法的数值逼近解算法。算法的可行性及通用性,在求解基准的复杂最优消费组合问题上得到了检验。     

状态变化下的连续时间动态投资组合选择

运用两状态隐马尔可夫模型刻画金融资产收益率序列的非线性变化,建立状态变化下的连续时间动态投资组合模型,利用动态规划得到最优投资决策的一般解,使用蒙特卡罗方法模拟投资者的投资决策行为.仿真结果表明:状态变化产生了对冲需求,对冲组合的大小依赖于投资者对市场状态的预期;当风险资产的波动率越小时,投资者状态信念的轻微变化都会引起对冲组合较大幅度的变化;当风险厌恶程度越大时,对冲组合对初始状态信念的变化越不敏感.     

具有异常波动市场的消费与投资策略

讨论了异常波动市场中容许借贷的消费与投资策略问题,阐述了随机最优控制理论应用于现代金融理论研究中的一种方法.首先给出了金融市场中不确定性的随机模型,利用It^o公式,得到了与消费及投资策略有关的财富过程的随机微分方程,并建立了最优消费与投资问题的随机控制模型.根据随机最优控制理论,导出了目标函数满足的Hamilton-Jacobi-Bellman(HJB)方程.通过对HJB方程的讨论,得到了最优消费与投资策略的分段表示函数,并就Hara效用函数进行讨论,得到了具体的消费与投资策略.     

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.     

基于风险价值约束的动态均值-方差投资组合的研究

研究了基于风险价值约束的动态均值-方差项目投资组合的数学模型,该模型是控制带约束的随机线性二次型（LQ）控制问题.在讨论该随机LQ控制问题的解之后,给出投资组合动态数学模型对应的随机哈密顿-雅克比-贝尔曼方程的解,得出了有效边界和最佳策略,讨论了风险价值约束的影响.最后,针对某油田勘探开发项目的实际情况,应用上述结论求出该实例的解,并讨论了风险价值约束发挥的作用.     

A multiple objective stochastic portfolio selection problem with random Beta

When selecting a portfolio, we need to consider, in general, the portfolio return and portfolio risk. Many risk measures have been used in portfolio selection problems as the Beta risk measure, introduced by the capital asset pricing model. Most of the existing research papers suppose that security's Beta has a deterministic value. Recently, many researchers argued that in selecting the optimal portfolio, securities’ Beta should be considered as an uncertain parameter. In this paper, we set up fundamentals to model the portfolio's Beta as a random variable and propose a multiple objective stochastic portfolio selection model with random Beta. To solve the proposed model, we apply a stochastic goal programming approach. A numerical example from the US stock exchange market is reported.     

Optimal consumption and portfolio choice with ambiguity and anticipation

This paper, adopting the recursive multiple-priors utility, studies the optimal consumption and portfolio choice in a Merton-style model with anticipation when there is a difference between ambiguity and risk. The fundamental issue is what the effects of ambiguity and anticipation on the investor’s behavior are. In the case of a logarithmic felicity function, the paper also shows that no hedging demand arises that is affected by both ambiguity and anticipation. Finally, the optimal portfolio is derived in terms of Malliavin derivatives and stochastic integrals.     

An stochastic multiattribute acceptability analysis‐based method for the multiattribute project portfolio selection problem with rank‐level information

In many cases of practical multiattribute project portfolio selection problems, it is hard to obtain accurate measurements of attributes and precise preference information. Even after a long and costly information gathering, the attribute measurements and the preference information can still be uncertain or inaccurate. Considerable cost saving will be obtained if the selection of an optimal project portfolio can be done using rank‐level information based on some or all the attributes, without knowing the preference information. In this paper, we propose a stochastic multiattribute acceptability analysis‐based method that can deal with mixed rank and cardinal attribute measurements and uses little or no weight information. In the proposed stochastic multiattribute acceptability analysis‐based method, the decision makers need not to express their preferences explicitly or implicitly, so it is particularly useful when no weight information is available at all. A numerical example involving selection of photovoltaic plants in an industrial province in Eastern China is provided to demonstrate the proposed method.     

Portfolio selection problem with nonlinear wealth equations under non-extensive statistical mechanics for time-varying SDE

This paper is dedicated to the study of continuous-time mean–variance optimal portfolio selection problem with non-linear wealth equations under non-extensive statistical mechanics for the time-varying stochastic differential equation model. Firstly, we allow the returns and variance of risky assets are time-varying functions, which can fit the financial data better. Secondly, we consider an investor with the non-linear wealth equation. In fact, the wealth equations are not linear in many cases. The investor has to pay some taxes, which leads to a non-linear wealth equation. Moreover, since the return of the stocks price may be affected by a large investors portfolio selection, the wealth equation is non-linear in this case. Thirdly, the non-linear wealth equation driven by Tsallis distribution is constructed under non-extensive statistical mechanics, which can capture the characteristics of fat tails and aiguilles of the risky asset’s return. The viscosity solution of the HJB equation for the portfolio problem is proposed by the optimal stochastic control theory and Lagrange multiplier method. Finally, the efficient portfolio strategy and efficient frontier under non-extensive statistical mechanics are obtained. Furthermore, numerical analysis and real data study are discussed to show our results.     

Mean–variance portfolio selection based on a generalized BNS stochastic volatility model

We study a mean–variance portfolio selection problem via optimal feedback control based on a generalized Barndorff-Nielsen and Shephard stochastic volatility model, where an investor trades in a generalized Black–Scholes market. The random coefficients of the market are driven by non-Gaussian Ornstein–Uhlenbeck processes that are independent of the underlying multi-dimensional Brownian motion. Our contribution is to explicitly compute and justify optimal portfolios over an admissible set that is large enough to cover some important classes of strategies such as the class of feedback controls of Markov type. Concretely, the mean–variance efficient portfolios and efficient frontiers are explicitly calculated through the method of generalized linear-quadratic control and explicitly constructed solutions to three integro-partial differential equations under a quite mild condition that only requires one stock whose appreciation-rate process is different from the interest-rate process. Related minimum variance issue is also addressed via our main results.     

考虑交易费的融资与分红最优控制模型

在实际金融市场中股份公司在红利分配和再融资过程中都需要支付固定交易费和比例交易费 ,而如何确定交易费对公司财务决策的影响还没有进行过讨论 .本文利用随机脉冲控制理论研究了在收取固定和比例交易费的市场环境下 ,公司如何制定其最优的财务策略 .首先给出了最优控制问题对应的Hamilton_Jacobi_Bellman方程 ,接着构造出了它的连续可微解 .利用解的性质和推广的It^o公式 ,构造出了最优的再融资及分红策略 .最后对模型的应用做了经济学上的解释 ,并与已有模型做了比较