不确定市场条件下的稳健最优投资组合

本文假设风险资产和无风险资产收益的相关参数属于某个已知的凸多面体,分别讨论了在市场不存在无风险资产和存在无风险资产的情况下稳健最优投资组合问题,给出了问题的解析解,从而推广了Markowitz均值-方差模型的结果.     

协差阵奇异时的最优投资组合

给出了协差阵半正定且有n-r个零特征值的一般情况下,Markowitz均值——方差最优投资组合模型的解及由单纯形表求得n-r个无风险基金权重的最优解.     

“安全第一”下的不连续价格过程的投资组合问题

主要研究了"安全第一"原则下的连续时间随机过程的投资组合问题,所考察的模型是带有布朗运动和跳跃扩散的随机过程.推导出了相应的哈密顿雅克比贝尔曼方程.当不存在无风险资产时,得出了最优投资策略的闭环解.同样讨论了存在无风险资产投资时的最优投资策略.最后给出了一个实例加以说明此模型和方法的有效性和可行性.     

CEV模型下家庭最优投资决策问题

考虑固定收入下具有随机支出风险的家庭最优投资组合决策问题.在假设投资者拥有工资收入的同时将财富投资到一种风险资产和一种无风险资产,其中风险资产的价格服从CEV模型,无风险利率采用Vasicek随机利率模型.当支出过程是随机的且服从跳-扩散风险模型时,运用动态规划的思想建立了使家庭终端财富效用最大化的HJB方程,采用Legendre-对偶变换进行求解,得到最优策略的显示解,并通过敏感性分析进行验证表明,家庭投资需求是弹性方差系数的减函数,解释了家庭流动性财富的增加对最优投资比例呈现边际效用递减趋势.     

跳-扩散风险模型的最优投资策略和破产概率研究

对盈余投资于金融市场的跳-扩散风险模型的最优投资策略和破产概率进行了研究,得到最优投资策略和最小破产概率的显示解,发现破产概率满足Lundberg等式．最后通过数值计算,得到最小破产概率与无风险利率,投资和相关系数之间的关系,以及无风险利率和相关系数对最优投资策略的影响．     

在不允许卖空条件下的最优比例再保险投资

假设保险公司的盈余过程服从一个带扰动项的布朗运动,保险公司可以投资一个无风险资产和n个风险资产,还可以购买比例再保险,并且风险市场是不允许卖空的.本文在均值一方差优化准则下研究保险公司的最优投资一再保策略选择问题,利用LQ随机控制方法求解模型,得到了保险公司的最优组合投资策略的解析和保险公司投资的有效投资边界的解析表达...     

贝叶斯方法在养老基金资产负债管理中的应用

把一个静态资产负债管理模型———均值方差模型应用到定额给付养老金计划的资产负债管理中,在允许无风险借贷的条件下研究养老金在无风险资产和风险资产间的分配问题,用定量分析的方法求出了最优投资组合的一般形式;又针对投资收益率特征参数未知的情况,提出了矩估计和贝叶斯估计两种方法求解最优资本配置比例,将两种方法的结果与一般形式对比,分析了影响最优投资组合的因素,得知养老基金在风险资产中的投资比例与基金经理对风险的厌恶程度、风险资产的风险益酬、风险资产收益率的波动性成负相关关系;并且随决策者掌握的历史信息增加,在风险资产上的投资比例也随之增加,投资行为逐渐趋于理性化;对上述结果进行仿真,验证了结论的有效性。     

一类投资组合选择的线性规划方法研究

如何在摩擦市场下构建最优组合一直是一个非常有意义的问题.人们通常在有效前沿上选择最优的投资组合,但是值得注意的是,如果我们考虑摩擦因素,原本的有效组合将不再有效.探讨如何在无风险借贷利率不同的摩擦市场下构建投资组合模型.为了得到最优策略,我们先利用Karush-Kuhn-Tucker条件给出一类线性规划问题求解方法,然后具体阐述如何将投资决策问题转化为可以求解的线性规划问题,最后给出在无风险借贷利率不同的情况下投资组合的有效边界.     

基于股票价格随机脉冲模型的保险人再保险和投资的最优动态组合选择

本文假设保险人可以进行再保险,并且允许其在金融市场中将资产投资于风险资产和无风险资产,其中风险资产价格采用随机脉冲模型来刻画.当目标是最大化在某一确定终止时刻所拥有财富的二次效用函数期望时,分别得到了超额损失再保险和比例再保险情况下保险人的再保险和投资最优动态选择的显式解和闭解.利用得到的显式解,考虑了金融风险和保险风险之间相关性对最优动态选择的影响,做了相关数值计算.     

Heston随机波动率模型下的资产负债管理问题

应用随机最优控制方法研究Heston随机波动率模型下带有负债过程的动态投资组合问题,其中假设股票价格服从Heston随机波动率模型,负债过程由带漂移的布朗运动所驱动.金融市场由一种无风险资产和一种风险资产组成.应用随机动态规划原理和变量替换法得出了上述问题在幂效用和指数效用函数下最优投资策略的显示解,并给出数值算例分别分析了市场参数在幂效用和指数效用函数下对最优投资策略的影响.     

Real-Time Solution of Bi-Level Optimal Control Problems

Bi-level optimal control problems are presented as an extension to classical optimal control problems. Hereby, additional constraints for the primary problem are considered, which depend on the optimal solution of a secondary optimal control problem. A demanding problem is the numerical complexity, since at any point in time the solution of the optimal control problem as well as a complete solution of the secondary problem have to be determined. Hence we deal with two dependent variables in time. The numerical solution of the bi-level problem is illustrated by an application of a container crane. Jerk and energy optimal trajectories with free final time are calculated under the terminal condition that the crane system comes to be at rest at a predefined location. In enlargement additional constraints are investigated to ensure that the crane system can be brought to a rest position by a safety stop at a free but admissible location in minimal time from any state of the trajectory. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear programming in measure spaces

This paper studies a linear programming problem in measure spaces (LPM). Several results are obtained. First, the optimal value of LPM can be equal to the optimal value of the dual problem (DLPM), but the solution of DLPM may be not exist in its feasible region. Sccond, :he relations between the optimal solution of LPM and the extreme point of the feasible region of LPM are discussed. In order to investigate the conditions under which a feasible solution becomes an extremal point, the inequality constraint of LPM is transformed to an equality constraint. Third, the LPM can be reformulated to be a general capacity problem (GCAP) or a linear semi-infinite programming problem (LSIP = SIP), and under appropriate restrictioiis, the algorithm developed by the authors in [7] and [8] are applicable for developing an approximation scheme for the optimal solution of LPM     

Two new algorithms for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities

This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions. Also, an efficient algorithm is proposed to solve the model based on the structure of FRI path, the concept of partial solution, and the branch-and-bound approach. The algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions. Some sufficient conditions are given that under them, some of the optimal components of the model are directly determined. Some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions. Then the reduced domain is decomposed (if possible) into several sub-domains with smaller dimensions that finding the components of the optimal solution in each sub-domain is very easy. In order to obtain an optimal solution of the original problem, we propose another more efficient algorithm which combines the first algorithm, these procedures, and the decomposition method. Furthermore, sufficient conditions are suggested that under them, the problem has a unique optimal solution. Also, a comparison between the recently proposed algorithm and the known ones will be made.     

The solution and sensitivity of a general optimal control problem

A solution method for the general optimal control problem is presented. This can be used to solve optimal control problems for which the system dynamics are not necessarily described by differential or difference equations. Having obtained the solution it is of theoretical and practical interest to investigate the sensitivity of the optimal trajectory to perturbations. Indicators of this sensitivity are the adjoint variables derived in the maximum principle. A method of deriving the adjoint variables from the solution is described. To illustrate the solution method and the determination of the adjoint variables a problem in the urban housing market is used.     

A Differential Games Solution to a Logarithmic Advertising Model

A logarithmic excess-advertising model of a duopoly is presented, and Nash optimal open-loop advertising strategies are determined. It turns out that if the two firms use different discount rates, then the optimal strategies will be exponentially decreasing. However, in this case the state equation has no nice solution and must be solved by numerical methods. When both firms use the same discount rate, then the state equation has a simple solution. This solution is also valid for the case where no discounting is performed. Furthermore, when no discounting is performed, the optimal strategies will be simple time-linear decreasing strategies. Finally, it is studied how the optimal strategies and trajectories depend on the parameters of the model.     

An Objective Penalty Function of Bilevel Programming

Penalty methods are very efficient in finding an optimal solution to constrained optimization problems. In this paper, we present an objective penalty function with two penalty parameters for inequality constrained bilevel programming under the convexity assumption to the lower level problem. Under some conditions, an optimal solution to a bilevel programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the objective penalty function, an algorithm is developed to obtain an optimal solution to the original bilevel programming, with its convergence proved under some conditions.     

一类不可微规划的多项式型算法

本文考虑了由教育最优投资问题导出的一类不可微规划，讨论了可行解是最优解的充要条件，在对乘子作某些假设下，利用Kuhu－Tucker定理给出了求解的一种多项式算法．     

Dynamic programming and the Hamilton-Jacobi method of classical mechanics

The conventional dynamic programming method for analytically solving a variational problem requires the determination of a particular solution, the optimal value function or return function, of the fundamental partial differential equation. Associated with it is another function, the optimal policy function. At each point, this function yields the value of the slope of the optimal curve to that point (or from that point, depending on the method of solution). The optimal curve itself can then be found by integration. In this paper, dynamic programming concepts and principles are used to develop two alternatives to the conventional method of solution. In the first method, a particular solution of two simultaneous partial differential equations is used to generate optimal curves by differentiations and solution of simultaneous equations. In the second method, any solution of the fundamental equation containing an appropriate number of arbitrary constants is sought. It is shown how such a function yields directly, by differentiations and solution of simultaneous equations, the optimal curve for a given problem. While the derivations to follow are new, the results are equivalent to those of a method due to Hamilton and its modification due to Jacobi.This work was completed by the author during the time of his association with the RAND Corporation Santa Monica, California.     

An inverse eigenvalue problem and an associated approximation problem for generalized K-centrohermitian matrices

A partially described inverse eigenvalue problem and an associated optimal approximation problem for generalized K-centrohermitian matrices are considered. It is shown under which conditions the inverse eigenproblem has a solution. An expression of its general solution is given. In case a solution of the inverse eigenproblem exists, the optimal approximation problem can be solved. The formula of its unique solution is given.     

带时变生产成本的易变质经济批量模型的最优策略分析

考虑了具有时变生产成本的易变质产品经济批量模型．有限计划期内,单位生产成本、生产率以及需求率假定为时间的连续函数,生产固定成本则具有遗忘效应现象．当不允许缺货时,建立了以总成本最小为目标的混合整数优化模型并证明了此问题最优解的相关性质．对于此问题的特殊情形,将成本函数中的离散型变量松弛为连续型变量,通过分析其最优解的存在性及唯一性,求解了此最优解,将其作为初始值设计了求取一般情形最优解的有效算法．最后通过算例验证了理论结果的有效性．