STABILITY OF THE UTILITY MAXIMIZATION PROBLEM WITH RANDOM ENDOWMENT IN INCOMPLETE MARKETS

We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. Simple sufficient conditions are given for the problem to be well posed, in the sense that the optimal wealth and the marginal utility‐based prices are continuous functionals of preferences and probabilistic views.     

数学建模教学改革的探索与实践

传统的教学模式具有较强的封闭性和保守性,忽略了数学思想的建立、数学方法的使用和学习能力的培养。《数学建模》具有难度大、涉及面广、形式灵活等特点,不易于培养学生的自主精神。学生普遍反映概念难懂,习题难做,方法不易掌握,自己建模有难度。虽然这门课程越来越受重视,但在教学中存在着问题。因此,在有限的课时内,如何组织安排好课堂的教学,进行教学方法的改革十分必要,且势在必行。     

Optimal high-frequency trading with limit and market orders

We propose a framework for studying optimal market-making policies in a limit order book (LOB). The bid–ask spread of the LOB is modeled by a tick-valued continuous-time Markov chain. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for obtaining execution order priority, which is a crucial issue in high-frequency trading. The agent faces an execution risk since her limit orders are executed only when they meet counterpart market orders. She is also subject to inventory risk due to price volatility when holding the risky asset. The agent can then also choose to trade with market orders, and therefore obtain immediate execution, but at a less favorable price. The objective of the market maker is to maximize her expected utility from revenue over a short-term horizon by a trade-off between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/impulse control problem that we characterize in terms of a quasi-variational system by dynamic programming methods. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. We provide an explicit backward splitting scheme for solving the problem and show how it can be reduced to a system of simple equations involving only the inventory and spread variables. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders.     

模糊综合评价在企业战略定位中的应用研究

根据企业经营战略SWOT矩阵分析原理设计了一套用于企业经营战略选择和评价体系，并利用模糊综合评价模型给出企业经营战略评价的方法。     

脂松引种的初步研究

利用数理统计方法,通过分析试验中得到的数据,讨论了脂松在黑龙江省城市引种的抚育管理技术,并分析了它的生长规律。     

Drainwater Management for Salinity Mitigation in Irrigated Agriculture

Salinity and drainage management options include source control, reuse, and evaporation ponds. This article identifies efficient strategies to maintain hydrologic balance in closed drainage basins and evaluates their impact on regional agricultural profits. Theoretical analysis suggests that economic efficiency requires acknowledgment of the nonseparability between water use and land value. Empirically, our solution involves a modest amount of source control, a substantial amount of reuse, and the elimination of evaporation ponds often associated with large environmental damages, while maintaining grower income. Various policy instruments and options are introduced and discussed, including a system of drainwater charges, marketable permits, and land retirement.     

数学建模与创新应用型人才培养

培养具有创新精神的应用型人才已经成为很多大学的办学目标,数学建模正是培养学生创新精神与实践能力的有效方法。     

双线性有限元Monte Carlo方法

本文构造了矩形有限元的概率算法,应用这种方法可以直接求出有限元解在一个或少数几个网格点的近似值。     

自卸汽车加伍德式举升机构优化设计数学模型

文章建立了自卸汽车加伍德式举升机构优化设计数学模型,给出了其优化设计目标函数min(KO)=min[(XG·DAEC)/(DOEC·DAEB)]和其评价指标α=Pmax/P-1,并介绍了约束条件的给出方法以及本优化设计数学模型的应用注意事项,为企业的自卸汽车设计提供了一套良好的设计方法。