Ornstein-Uhlenbeck模型下DC养老金计划的最优投资策略

本文研究了Ornstein-Uhlenbeck模型下确定缴费型养老金计划(简称DC计划)的最优投资策略,其中以最大化DC计划参与者终端财富(退休时其账户金额)的CRRA效用为目标.假定投资者可投资于无风险资产和一种风险资产,风险资产的瞬时收益率由Ornstein-Uhlenbeck过程驱动,该过程能反映市场所处的状态.利用随机控制理论,给出了相应的HJB方程与验证定理;并通过求解相应的HJB方程,得到了最优投资策略和最优值函数的解析式.最后分析了瞬时收益率对最优投资策略的影响,发现当市场向良性状态发展时,投资在风险资产上的财富比例呈上升趋势;当初始财富足够大且市场状态不变时,投资在风险资产上的财富比例几乎不受时间的影响.     

跳-扩散风险模型的最优投资和再保险策略

本文对跳-扩散风险模型,在赔付进行比例再保险,以及盈余投资于无风险资产和风险资产的条件下,研究使得最终财富的指数期望效用最大的最优投资和比例再保险策略.得到最优投资策略和最优再保险策略,以及最大指数期望效用函数的显式表达式,发现最优策略和值函数都受到无风险利率的影响.最后通过数值计算,得到最优投资和比例再保险策略,以及值函数与模型各个参数之间的关系.     

Optimal Market Making in the Foreign Exchange Market

Abstract

This paper is concerned with optimal market making in the foreign exchange market. The market maker's holdings in the different currencies are modelled as stochastic processes that are influenced by both the stochastic exchange rates and the stochastic customer buy and sell orders. The market maker can control their own bid and ask price quotes and, additionally, can buy and sell at other market participants' quotes. The resulting stochastic control problem consists of a controlled diffusion problem for the optimal quotes and a singular control problem for optimal trades at other market participants' quotes. A Markov chain approximation is used to derive optimal strategies.     

基于灰色马尔可夫预测模型的农村人均收入预测

以武汉市农村人均收入为样本,将灰色预测模型和马尔可夫链预测模型相结合,通过对比预测的数据信息与实际数据信息差距,对2011年和2012年武汉市农村人均收入进行了预测计算.根据相关模拟检验与残差修正,灰色马尔可夫链可视为农村人均收入预测的可行且有效的方法.结果显示,单纯地运用灰色模型,预测值与实际值的误差均值是0.687%;通过马尔可夫链模型的二次模拟得到的误差明显减小.     

决策依赖不确定条件下基于复合实物期权估值的工程系统投资决策研究

不确定性是复杂工程系统的内在属性,在决策依赖不确定条件下对工程系统的投资决策需考虑不确定性与决策过程之间的交互作用,使得投资决策问题的求解非常困难.提出了决策依赖不确定条件下复合实物期权估值的最小二乘模拟算法,方法较好地解决了在决策依赖不确定条件下由于不同期权价值相互耦合所带来的计算复杂性,进一步拓展了最小二乘模拟算法在期权估值中的应用,基于该方法,可以比较方便地解决决策依赖不确定条件下工程系统投资决策问题.     

工薪类个税征收标准对调节居民收入分配作用的统计分析

个人所得税一直是中国老百姓最关注的话题之一,2011年个税征收标准改革的问题再次引起大家的关注,主要焦点集中在工资、薪金类的个税征收的起征点和累进税率。本文选择2001至2010年31个省份的19行业的平均工资为基础数据,运用SPSS统计分析软件分别按省份和行业作为因子对税前和税后的平均工资做方差分析,利用假设检验的P值构造统计量,定义了调节比和调节得分两个评价指标,用这两个指标衡量个人所得税征收标准对缩小工资差距的效用。本文中该模型把个税征收标准对调节居民收入分配的效果数量化,通过得分指标的变动说明过去两次个税征收标准调整的必要性以及今年审议的第四套个人所得税征收标准草案的优劣。还可以通过该模型构建的指标对某套个人所得税的征收标准是否适应当前经济发展需要起到参考作用。     

基于股价服从对数正态分布的凯利投资策略

基于集中投资策略的思想,把股票价格服从对数正态分布与凯利优化模型相结合,使其能更好地运用于股票投资实践中,推导出投资者个股投资的资产配置比例与投资者对个股投资收益率和标准差预测值之间的数学关系,从而实现最快财富增长速率的目标.     

Theory of Economic Equilibrium

Abstract

New concepts of economics such as an average demand matrix of society, strategy of a firm and consumer behaviour, and others are introduced. We give sufficient conditions for technological mapping under which there exist both the Walras equlibrium state and optimal Walras equilibrium one. We obtain the set of equations which equilibrium price vector solves. The theory of interindustry economic equilibrium is developed. The model of economy with regular interests of consumers is proposed.     

Numerical solution of an optimal investment problem with proportional transaction costs

This paper mainly concerns the numerical solution of a nonlinear parabolic double obstacle problem arising in a finite-horizon optimal investment problem with proportional transaction costs. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints and the properties of the utility function allow to obtain the optimal investment solution from a nonlinear problem posed in one spatial variable. The proposed numerical methods mainly consist of a localization procedure to pose the problem on a bounded domain, a characteristics method for time discretization to deal with the large gradients of the solution, a Newton algorithm to solve the nonlinear term in the governing equation and a projected relaxation scheme to cope with the double obstacle (free boundary) feature. Moreover, piecewise linear Lagrange finite elements for spatial discretization are considered. Numerical results illustrate the performance of the set of numerical techniques by recovering all qualitative properties proved in Dai and Yi (2009) [6].