Table of Content

15 March 2016, Volume 20 Issue 1

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Portfolio selection models with new negative exponential expected utilities

FU Tianwen, TU Zhuozhuo, WEI Boyang

2016, 20(1):  1-18.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.001

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With an overview of the literatures on discussions about optimal investment decision problems, we propose a new class of negative exponential utility function satisfying the monotonicity and concavity. And reasonable explanations are also given from the viewpoints of mathematics and economics. The fat-tail phenomenon of the loss distribution is controlled efficiently by different kinds of weighted function and proper description to the tail. We use L-statistics to estimate the new expected utility and the rationality is also illustrated. Moreover, we construct a realistic portfolio selection model with multiple market frictions. With the real data from Chinese and American stock market, we carry out a series of empirical studies. Empirical results show the superiority and robustness of our new expected utility.

Optimal pension investment problem with stochastic salary

杨鹏

2016, 20(1):  19-30.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.002

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Under three kinds of objective function, optimal pension investment problem with stochastic salary is studied. The first objective function is mean-variance criterion. The second is stochastic differential game based on utility. The third is stochastic differential game based on mean-variance. During stochastic differential game, the both sides of game are the pension plan investors and financial markets, and financial market is a game of virtual hand. Under three kinds of objective function, closed-form solutions for the value function are obtained by applying linear quadratic control theory as well as the optimal strategies.

Three-echelon supply chain scheduling problem with learning effect

LIU Ying, ZHANG Xingong

2016, 20(1):  31-42.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.003

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This paper studies three-echelon supply chain scheduling problem with learning effect.  Multiple customers are distributed in different locations. And some orders of each customer will be processed in manufacturers. Manufacturers need to purchase the corresponding raw materials from different places to process the different orders of different customers.  Finally,  the processed orders need to be transported the corresponding customer by limited transportation vehicles.  The transportation vehicles will transport goods as possible as truck load.  We present the three dynamic programming to solve the problems of maximum flow time,  total flow time and maximum lateness.

Path-following interior point algorithms based on wide neighborhoods and a new class of directions

LIU Changhe, SHANG Youlin, LI Jinrui

2016, 20(1):  43-53.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.004

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This paper presents a class of path-following interior point algorithms for the monotone linear complementarity problems based on wide neighborhoods and the new directions with a parameter \theta. When the parameter \theta=1, the new direction is exactly the classical Newton direction. The algorithms have O(nL) iteration complexity when the parameter \theta is independent of the dimension n, which coincides with the best known iteration complexity for the classical wide neighborhood algorithms. When \theta=\sqrt{n/\beta\tau}, the algorithm has O(\sqrt{n}L) iteration complexity, the best iteration complexity obtained so far by any interior point method for solving linear complementarity problems, where \beta and \tau are neighborhood parameters. To our knowledge this is the first time that a class of interior point algorithms including the classical wide neighborhood path-following algorithm is proposed and analyzed.

Weak S-efficient solution of vector optimization

GUO Hui, BAI Yanqin

2016, 20(1):  54-60.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.005

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In this paper, we introduce the concept of weak S-optimal solution and S-subconvexlikeness of vector optimization with set-valued maps and obtain an alternative theorem in a real locally Hausdorff topological vector space. Furthermore, under the assumption of S-subconvexlikeness, we establish scalarization theorem for weak S-efficient solution. We also give some examples to illustrate the main results.

Integration of mathematical programming with constraint programming for multi-objective planning and scheduling

GONG Jing

2016, 20(1):  61-74.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.006

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Planning and scheduling, a NP-hard problem, can be viewed as a decision-making process of allocating limited resources to tasks over time with the goal of optimizing a certain objective. Neither mathematical programming nor constraint programming can solve it in the reasonable time. Minimum cost, minimum makespan and minimum tardiness are three classical objectives for this problem. The requirements from a real world application might be that several goals need to be achieved simultaneously. Based on Benders decomposition approach, this paper proposed an algorithm integrating  mathematical programming and constraint programming for solving multi-objective planning and scheduling.

Stability of optimal solution set and optimal value for minimax stochastic programming approximation problems

HUO Yongliang

2016, 20(1):  75-83.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.007

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In this paper, we research convergence of minimax approximation problems  of special class of bilevel stochastic programming. First, under regularity conditions of feasible set, we expand optimal solution set of lower level original stochastic programming to into non-singleton set. And we give continuity of optimal value and upper semi-convergence of the optimal solution  set on the upper level decision variables for lower level stochastic programming approximation problem. Furthermore, we feedback $\varepsilon$-optimal solution vector function provided by the lower level stochastic programming into the objective function of the upper level stochastic programming problems, and obtain the continuity of optimal value and the upper semi-convergence of optimal solution set with respect to the minimal information (m.i.) probability metric for upper level programming.

Online batch scheduling with known information in advance

WANG Chengfei, ZHANG Yuzhong

2016, 20(1):  84-90.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.008

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We study a single online batch scheduling problem with known information in advance. The information arrives over time and the objective is to minimize the maximum completion time. The time between the information arrival of a job and its release time is constant $a$. The maximum of the processing times of all jobs $p_{{\rm max}}$ is known in advance too. A batch processing machine can handle up to $b$ jobs simultaneously. The processing time of a batch is given by the longest processing time of all jobs in the batch. When $b=\infty$, we provide an optimal online algorithm $\gamma H^\infty$ with a competitive ratio of $1+\gamma$, where $\gamma=\left(-1+\sqrt{1+\frac{4p_{{\rm max}}}{p_{{\rm max}}+a}}\right)/2$.

Optimal excess-of-loss reinsurance and investment strategy under state-dependent utility function

GU Ailing, CHEN Shumin

2016, 20(1):  91-104.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.009

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This paper studies an optimal excess-of-loss reinsurance and investment problem for an insurer, and aims to maximize the expected exponential utility from her terminal wealth with a state-dependent utility function. It is assumed that the surplus of the insurer and the financial market are modulated by an observable continuous-time Markov chain. By applying stochastic control theory, the explicit expression of  optimal reinsurance-investment strategy is obtained. Finally, the impact of some parameters on the optimal strategy and optimal value function is given.

Determining the discriminating domain for linear differential games based on viability theory

HAN Yanli, GAO Yan

2016, 20(1):  105-111.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.010

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This paper studies a bounded discriminating domain for linear pursuit-evasion differential games using viability theory. Researching a bounded polyhedron who is a convex hull of finite points for the discriminating domain of linear differential games by viability theory, we just need to test whether the extreme points of the polyhedron meet the viability conditions. Then, using the relationship between viability and discriminating domain, we can determine whether the polyhedron is the discriminating domain of the differential games. It is easy to be used.

The Hamilton-connectivity with the degree sum of  non-adjacent subgraphs P_ 4 and K_1 in claw-free graphs

ZHENG Wei, WANG Ligong

2016, 20(1):  112-117.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.011

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This paper studies the relationship between the degree of subgraphs and Hamiltonicity of graphs. It is proven that every 3-connected claw-free graph $G$ of order $n$ with minimum degree $\delta(G)\geq4$ is Hamilton-connected if it satisfies $d(H_1)+d(H_2)\geq n$ for any two non-adjacent subgraphs $H_1$, $H_2$ which are isomorphic to $P_4$, $K_1$ respectively.

Continuity of the solution set map to parametric weak vector equilibrium problems

LUO Guowang, PENG Yanfang, LIU Yanmin, HUANG Jianwen

2016, 20(1):  118-124.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.012

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In this paper, using the nonlinear scalarization method, we obtain the upper semicontinuity and lower semicontinuity of the solution mappings to parametric weak vector equilibrium problems. Some examples are given to illustrate our results.

Some results on fractional k-factor-critical graphs and fractional k-extendable graphs

HUANG Xiaoxian, LIU Yan, WU Bosi

2016, 20(1):  125-130.  doi:10.15960/j.cnki.issn.1007-6093.2016.01.013

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 A simple graph G is said to be fractional k-factor-critical if after deleting any k vertices, the remaining subgraph still has a fractional perfect matching. A graph G is called a fractional k-extendable graph if G has a fractional perfect matching containing M for any k-matching M. In this paper, a sufficient condition for a graph to be fractional k-factor-critical graph and fractional k-extendable graph is given, respectively. Besides, a sufficient and necessary condition for a graph to be fractional k-factor-critical graph is given.