最优投资消费策略

投资消费问题是数理金融中的一个主要问题,Merton在假设股票价格过程为扩散过程的情形下,给出了最优投资消费策略的显式解,本在股份价格过程为跳－扩散过程的情形下,讨论了最优投资消费策略问题,得到了最优投资消费策略的偏微分方程。     

Heston随机波动率模型下的动态投资组合

应用随机最优控制方法对Heston随机波动率模型下的动态投资组合问题进行了研究,得到了幂效用和指数效用下最优投资策略的显示解,并给出一些数值计算结果分析了市场参数对最优投资策略的影响.     

多维分数布朗运动环境下的最优投资组合问题

在分数布朗运动环境下,讨论了单资产多噪声情形下的最优投资组合问题.假定标的资产价格遵循多维分数布朗运动驱动的常系数随机微分方程,在给定效用函数分别为幂函数和对数效用函数条件下,得到了最优投资组合问题的显式解.     

单时期证券市场的最优投资组合

考虑了单时期金融市场模型的最优投资组合问题,并对一般的效用函数,给出了最优投资组合问题有解的一个充分条件.     

最优投资组合模型研究

本文研究了在完备金融市场上 ,投资者最优投资组合的随机模型。在模型参数为常系数 ,效用函数为 (0 ,T],B[0 ,T])上的有界可测函数的情形下 ,得出其最大效用值函数是随机控制问题对应的 HJB方程的平滑解 ;最优策略被证明是存在的 ,并用反馈形式给出了最优投资组合策略。     

基于几何布朗运动的投资组合模型

在证券的价格过程是几何布朗运动的前提下,建立了最优投资组合的多目标规划模型,使得投资收益最大和投资风险最小,并利用线性加权和法求得有效解.最后用实例进行分析.     

一类证券市场中投资组合及消费选择的最优控制问题

研究一类证券市场中投资组合及消费选择的最优控制问题．在随机干扰源相互关联情形下,运用动态规划方法,对一类典型的效用函数CRRA(Constant Relative Risk Aversion,常数相对风险厌恶)情形,得到了最优投资组合及消费选择的显式解,并给出了最优解的经济解释和关于部分参数的灵敏度分析．     

证券市场上含有多个基金时的最优投资策略

本文研究了证券市场中包含多个基金和股票时的均值-方差最优投资决策模型,得到了最优投资组合的解析表达形式,以及对应的投资有效前沿,证明了两基金分离问题,由于最优解是不唯一的,进而讨论了最优解集合的结构,并对实例进行计算与分析。     

保险公司的最优投资和再保险策略

在保险公司既可以做证券(股票和债券)投资,同时又采取比例再保险策略的情况下,通过对经典的Cramér-Lundberg保险公司盈余过程模型的连续扩散近似,利用动态规划原理分别得出了在破产概率最小和终值期望效用最大两种目标函数下,保险公司的最优投资和最优再保策略的显式解和对应的目标函数值.对两种目标函数下的最优策略做了比较研究.     

竞争条件下公司最优投资策略纳什均衡分析

大多数实物期权文献都只是研究一个公司在没有竞争条件下的最优决策,然而实际上竞争者的行为经常影响到公司的投资机会.通过建立投资概率是临界值的函数模型,根据期权博弈理论研究了在不确定条件和不同信息结构下,一个或多个公司的最优投资策略纳什均衡解,并用MATLAB语言对案例进行了仿真分析,画图说明了参数变化对投资策略的影响.     

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.     

Lagrange Multiplier Conditions Characterizing the Optimal Solution Sets of Cone-Constrained Convex Programs

Various characterizations of optimal solution sets of cone-constrained convex optimization problems are given. The results are expressed in terms of subgradients and Lagrange multipliers. We establish first that the Lagrangian function of a convex program is constant on the optimal solution set. This elementary property is then used to derive various simple Lagrange multiplier-based characterizations of the solution set. For a finite-dimensional convex program with inequality constraints, the characterizations illustrate that the active constraints with positive Lagrange multipliers at an optimal solution remain active at all optimal solutions of the program. The results are applied to derive corresponding Lagrange multiplier characterizations of the solution sets of semidefinite programs and fractional programs. Specific examples are given to illustrate the nature of the results.     

Least-Squares Mirrorsymmetric Solution for Matrix Equations （AX=B, XC=D）

In this paper, least-squaxes mirrorsymmetric solution for matrix equations (AX = B, XC = D) and its optimal approximation is considered. With special expression of mirrorsymmetric matrices, a general representation of solution for the least-squares problem is obtained. In addition, the optimal approximate solution and some algorithms to obtain the optimal approximation are provided.     

A Fast and Stable Algorithm for Linear Parabolic Partial Differential Equations

In the paper, a two-grid finite element scheme is discussed for distributed optimal control governed by elliptic equations. With this new scheme, the solution of the elliptic optimal control problem on a fine grid is reduced to the solution of the elliptic optimal control problem on a much coarser grid and the solution of a linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy. Finally, numerical experiments are carried out to confirm the considered theory.     

An achievement rate approach to linear programming problems with an interval objective function

In this paper, we focus on a treatment of a linear programming problem with an interval objective function. From the viewpoint of the achievement rate, a new solution concept, the maximin achievement rate solution, is proposed. Nice properties of this solution are shown: a maximin achievement rate solution is necessarily optimal when a necessarily optimal solution exists, and if not, then it is still a possibly optimal solution. An algorithm for a maximin achievement rate solution is proposed based on a relaxation procedure together with a simplex method. A numerical example is given to demonstrate the proposed solution algorithm.     

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.     

On the existence of dual solutions for Lorentzian cost functions

The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is further shown that the existence of a dual solution implies that the optimal transport is timelike on a set of full measure. In the second part the persistence of absolute continuity along an optimal transportation under obvious assumptions is proven and a solution to the relativistic Monge problem is provided.     

运输问题的改进算法探讨

探讨了运输问题表上作业法初始解的取得和最优解的判断，在一定程度上可以省略表上作业法的方案调整过程，从而简便了求解运输问题的最优解的过程。     

Active Constraint Set Invariancy Sensitivity Analysis in Linear Optimization

Active constraint set invariancy sensitivity analysis is concerned with finding the range of parameter variation so that the perturbed problem has still an optimal solution with the same support set that the given optimal solution of the unperturbed problem has. However, in an optimization problem with inequality constraints, active constraint set invariancy sensitivity analysis aims to find the range of parameter variation, where the active constraints in a given optimal solution remains invariant.For the sake of simplicity, we consider the primal problem in standard form and consequently its dual may have an optimal solution with some active constraints. In this paper, the following question is answered: “what is the range of the parameter, where for each parameter value in this range, a dual optimal solution exists with exactly the same set of positive slack variables as for the current dual optimal solution?”. The differences of the results between the linear and convex quadratic optimization problems are highlighted too.     

带随机过程的随机规划问题——最优值过程与最优解集过程的鞅性

假设问题中所含随机过程为鞅，本文证明了带随机过程的随机规划问题共最优值过程与最优解集过程分别为实值上鞅与集值上鞅，且存在最优鞅通过程。