Proportional share analysis

The purpose of this paper is to generalize the theory of “equal share analysis”, developed by Selten in 1972, to the one in which every player has a positive weight. We show that for any positive vector of weights, α∈R ₊₊ ^N , it is always possible to find a coalition structure and a payoff vector forming a proportional regular configuration.     

价格一致性系统与风险偏好

本文研究了风险偏好问题.利用简单市场模型,讨论了个人风险偏好和市场风险偏好,给出了两种风险偏好的数学定义,该定义具有自然直观的经济学意义.     

Measuring the relevance of the microstructure noise in financial data

We show that the Truncated Realized Variance (TRV) of a SemiMartingale (SM) converges to zero when observations are contaminated by noise. Under the additive i.i.d. noise assumption, a central limit theorem is also proved. In consequence it is possible to construct a feasible test allowing us to measure, for a given path of a given data generating process at a given observation frequency, the relevance of the noise in the data when we want to estimate the efficient   process integrated variance IV$IV$. We thus can optimally select the observation frequency at which we can “safely” use TRV. The performance of our test is verified on simulated data. We are especially interested in the application of the test to financial data, and a comparison conducted with Bandi and Russel (2008) and Ait-Sahalia, Mykland and Zhang (2005) mean square error criteria shows that, in order to estimate IV, in many cases we can rely on TRV for lower observation frequencies than previously indicated when using Realized Variance (RV). The advantages of our method are at least two: on the one hand the underlying model for the efficient data generating process is less restrictive in that jumps are allowed (in the form of an Itô SM). On the other hand our criterion is pathwise, rather than based on an average estimation error, allowing for a more precise estimation of IV because the choice of the optimal frequency is based on the observed path. Further analysis on both simulated and empirical financial data is conducted in Lorenzini (2012) [15] and is also still in progress.     

基于非参数估计方法的沪铜期货价格研究

非参数估计方法是现代统计学的一个新发展方向,在各领域有重要的应用价值.本文针对非参数模型的三种估计方法,将其应用于沪铜期价与LME现价的相关关系分析,得到模型的拟合值和拟合曲线.最后,与最小二乘法的结果进行比较分析,证实了非参数估计在不同历史时期有预测精度高的优点.     

Biobjective center – balance graph location model *

In the paper, a new algorithm for finding the absolute center of the graph is proposed. Later on problem of the absolute balance point of the graph is investigated the objective function of which is defined as the difference in the distance from the located facility to the farthest and the nearest demand point. An algorithm for finding it is presented By following the balance criterion it may happen, that the balance point is located too far from the demand points. Conversely, if we are interested not only in the distance to the farthest demand point, but (what is more realistic) also in the structure of the distances, a criterion of balance is appropriate. Consequently, we investigate the center balance constrained model that simultaneously used center and balance criteria. By considering the center and the balance objective in a multiobjective framework, efficient solutions are generated by minimizing former objective such that latter satisfies an upperbound     

Necessity of limiting co-state arcs in Bolza-type infinite horizon problem

We investigate necessary conditions of optimality for the Bolza-type infinite horizon problem with free right end. The optimality is understood in the sense of weakly uniformly overtaking optimal control. No previous knowledge in the asymptotic behaviour of trajectories or adjoint variables is necessary. Following Seierstad’s idea, we obtain the necessary boundary condition at infinity in the form of a transversality condition for the maximum principle. Those transversality conditions may be expressed in the integral form through an Aseev–Kryazhimskii-type formulae for co-state arcs. The connection between these formulae and limiting gradients of pay-off function at infinity is identified; several conditions under which it is possible to explicitly specify the co-state arc through those Aseev–Kryazhimskii-type formulae are found. For infinite horizon problem of Bolza type, an example is given to clarify the use of the Aseev–Kryazhimskii formula as an explicit expression of the co-state arc.     

The equitable dispersion problem

Most optimization problems focus on efficiency-based objectives. Given the increasing awareness of system inequity resulting from solely pursuing efficiency, we conceptualize a number of new element-based equity-oriented measures in the dispersion context. We propose the equitable dispersion problem that maximizes the equity among elements based on the introduced measures in a system defined by inter-element distances. Given the proposed optimization framework, we develop corresponding mathematical programming formulations as well as their mixed-integer linear reformulations. We also discuss computational complexity issues, related graph-theoretic interpretations and provide some preliminary computational results.     

Introduction to duality in optimization theory

A systematic exposition of duality theory is given on what appears to be the optimal level of generality. A condition is offered which implies that the ideal of duality theory is achieved. For the case of linear programming, our approach leads to two novel features. In the first place, primal and dual LP-problems and complementarity conditions are defined canonically, without choosing a matrix form. In the second place, without deriving the explicit form of the dual problem, we show that the following well-known fact implies that the condition mentioned above holds: the polyhedral set property is invariant under linear maps. We give a new quick algorithmic proof of this fact.The author would like to thank Jan Boone for his helpful comments on a preliminary version of this paper.     

Knight不确定下基于无穷纯跳Levy过程的一般风险资产的动态最小定价

研究了具有Knight不确定性的金融市场下的一般风险资产的动态最小定价,利用倒向随机微分方程(BSDE)理论以及时间-风险折现方法,推导出了基于无穷纯跳Levy过程的一般风险资产在实际概率测度下的动态定价公式及其在Knight不确定性控制集合上的动态最小定价.最后给出了一个欧式看涨期权动态最小定价的例子,并导出期权价格的显示表达式.在Knight不确定环境下,引入Levy过程来描述股票价格的动态走势,更加符合实际市场,可广泛地应用于一般风险资产的定价过程,这为投资分析提供一定的理论依据.