随机市场系数的M-V最优投资组合选择:一个鞅方法

通过引进凹函数U(x)以及等价鞅测度p^-，应用鞅的性质得到了随机市场系数情形下的M—V模型的最优投资策略以及有效前沿．     

完备市场下的均衡和财富优化

针对跳扩散模型中的优化与均衡问题,利用鞅方法和随机点过程理论,建立了跳扩散模型下的均衡市场,分析了市场中的财富优化问题,给出了均衡大宗商品现货价格、最优财富过程、最优投资组合及最优消费过程.     

连续市场下的增长最优投资策略

考虑由m 1个资产构成的金融市场,假定每一个资产的价格是严格正的It过程,这里不要求其中一个必须是债券(无风险资产).给出了增长最优投资策略(GOP)存在时,投资策略的比例所满足的必要条件,以及类似得到以不同的资产作为记账单位得到的折现增长最优投资策略存在时投资策略比例所满足的必要条件,并证明了这些比例之间满足一个固定的形式.同时在一定条件成立下,推出了增长最优投资策略的价格过程.若市场存在等价鞅测度,证明了以增长最优投资策略作为记账单位所对应的等价鞅测度就是客观概率测度P.     

不完全市场下考虑损失厌恶的连续时间投资组合选择

在不完全市场条件下研究了一般情形下的损失厌恶投资者的连续时间投资组合选择模型. 面对市场风险, 投资者的偏好由一个S-型的价值函数定义. 通过把不完全市场转换为完全市场, 利用鞅方法和复制技术, 分别获得了投资者的最优期末财富以及最优投资策略. 最后讨论了一个分段幂函数的例子, 在模型系数为确定的常数情形下, 得到了最优解的显示表达式.     

不完全市场下基于对数效用的动态投资组合

应用鞅方法研究不完全市场下的动态投资组合优化问题。首先,通过降低布朗运动的维数将不完全金融市场转化为完全金融市场,并在转化后的完全金融市场里应用鞅方法研究对数效用函数下的动态投资组合问题,得到了最优投资策略的显示表达式。然后,根据转化后的完全金融市场与原不完全金融市场之间的参数关系,得到原不完全金融市场下的最优投资策略。算例分析比较了不完全金融市场与转化后的完全金融市场下最优投资策略的变化趋势,并与幂效用、指数效用下最优投资策略的变化趋势做了比较。     

具有一般跳过程的期权无差异效用价值过程的定价模型

本文采用指数效用最大化的方法研究了期权的动态无差异效用价值过程Ct(H;α).考虑股票价格过程为具有基于随机测度的一般跳的半鞅模型,且期权的无差异效用价值过程的Doob-Meyer分解的鞅部分的GKW(Galtchouk-Kunita-Watanabe)分解满足Jacod鞅表示定理.利用无差异效用价值过程在最小熵测度和最优投资策略下为鞅的事实构建了一个倒向随机微分方程.通过概率测度变换将方程的鞅部分和生成元转化为BMO(bounded mean oscillation)鞅,证明了该方程的解的唯一性.并将方程的生成元分成[?A=0]和[?A≠0],证明了最优投资策略存在.从而给出期权无差异效用价值过程的倒向随机微分方程的表达形式.     

延迟索赔风险模型的最优投资策略

本文研究了延迟索赔风险模型最小化破产概率的最优投资决策问题.利用鞅中心极限定理将风险过程逼近为伊藤扩散过程,在此基础上将盈余投资于风险市场和无风险市场,采用随机马尔可大控制理论将其转化为相应的Hamilton-Jacobi-Bellman方程,获得了最优投资策略的显式表达式.得到的结果推广了延迟索赔风险模型的研究.     

部分信息下资产收益率发生紊乱的最优投资策略

本文研究了在部分信息且市场利率非零的情形下,资产预期收益率发生紊乱(disorder)时,终端净财富的期望指数效用最大化问题.利用半鞅和倒向随机微分方程(BSDE)刻画价值过程的方法,获得了最优交易策略和价值过程的明确表达式,推广了一般框架下最优投资组合的研究结果.     

奈特不确定下资产收益率发生紊乱的最优投资策略

在部分信息且市场利率非零的情形下,应用α-极大极小期望效用(α-MEU)模型区别投资者的含糊和含糊态度,研究资产预期收益率发生紊乱(disorder)时的投资组合问题.首先,利用倒向随机微分方程理论刻画了α-MEU.其次,给出紊乱时刻的后验概率过程满足的随机微分方程(SDE),以及价值过程所满足的倒向随机微分方程(BSDE).最后,应用鞅论解出指数效用时的最优交易策略和价值过程的明确表达式.     

随机利率下期权定价

本文在随机利率的基础上,考虑股票价格过程和利率过程分别为扩散过程和Ito过程,并且在相关的假设下,运用鞅方法推导出欧式期权价值过程所满足的微分方程;以及利率满足一种特殊方程时,运用最优停止的鞅方法,得到了随机利率下美式期权的价格和最优停时.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.