An Application of Hamilton-Jacobi-Bellman Equation in Optimal Investment

The simple portfolio investment model is given, with the HJB equation. The optimal portfolio investment problem is discussed under some given supposition, the quantitative relations are gotten between the investment strategies and riskless investment income rate and risk investment income rate are gotten. And with the quantitative relations, we study the qualitative relations between the investment strategies and riskless investment income rate and risk investment income rate. This also accounts for the effect of the falling interest rate of RMB on the national economy.     

Model of Real Estate Portfolio Investment Based on the Least Risk

The high-speed development demands new real estate investment theory. Using the experiences of the Western developed countries for reference in property investment and modern portfolio investment theory, the paper introduces the conception of systematic and unsystematic risk with the centre of risk and profit. Consequently, the model of real estate base on least risk and anticipated profit is studied in the discussion of its concerned hypothesis and determining the concerned parameters. With living example analysis, we reach the conclusion that portfolio investment risk is smaller than single investment if the investor adjusts the tactics of portfolio investment.     

A Caculation Method of Portfolio Investment under the Risk Mininiz

According to the security investment theory of Markowitz,this paper presents aCaculation method of portfolio investment under the risk minimization,and some mathematic expres-sions of the efficient frontier for portfolio investment are conducted.Based on these,the efficientfrontier is proved as a parabola,and a practical caculation process is given.     

Two Optimization Methods for Portfolio Investment Decision

On the basis of introducing some fundamental theories and computational methods of portfolio investment, this paper derives a decision model for searching optimal portfolio with the utility function. Then,after comparing the new model with the conditional extreme optimization model,which has been usually considered by people,the result shows the new model would be more efficient under certain conditions.     

Analysis of Portfolio -Effect in Tax Planning

The quantities of taxes, as an important and difficult factor of finance, influences directly profits that corporations really got. Tax planning in enterprises could be regard as one portfolio investment of securities. Being concerned of cost and risk, portfolio theory is used as a new way in study of tax planning to evaluate validity of planning program and make optimal choice to achieve the portfolio-effect which is more planning profits and less planning risks.     

Some Properties and Model of the Efficient Margin in Portfolio Combinatorial Investment

This paper proves some properties of the efficient margin in portfolio combinatorial investment and presents a methematical model for calculating the optimal weighted vector of portfolio combinatorial investment     

Information Structures in Portfolio Selection

This paper gives a brief presentation of the influence of different information structures on portfolio selection and some simple examples to demonstrate their basic algorithms. The first is the familiar mean_variance model. The model does not need more hypotheses on the motion of the asset price along the full continuous time axis,but sometimes many unanticipated computation problems may be involved because of the difficulty in computing the inverse of some matrices with high dimension. The second is the stochastic optimal control model. It is to solve a stochastic optimal control problem,which is often related to Hamilton_Jacobi_Bellman eqution.It results in solving partial differential equations of Riccati matrix differential equations. Their closed_form solutions are usually very hard to obtain. The last is the differential game model. The existence,uniqueness,and the computation for its equilibrium solution are all very difficult mathematical problems.     

Analysis on Strategies to Construct Portfolio Insurance

The strategies of portfolio insurance are introduced according to its principles and design thinking.The(authors) give the simple mathematical models and practical processes of option-based portfolio insurance(OBPI),constant mix(CM),constant proportion portfolio insurance(CPPI),and time-invariant portfolio protection(TIPP),and use risky assets containing 180 index's stocks of Shang-hai Stock Exchange and risky-free assets containing bonds to form portfolio to do empirical simulating.Based on the results,they analyze the above strategies comparatively,gives the(related) investment suggestion,and shows how to avoid risk without restriction on profit.     

Optimal Model of Portfolio under Safety-First Criteria and Portfolio Performance Management

We point out the shortage of optimal portfolio model which was suggested by Markowitz in 1952, this theory has been less useful in practice because one must know indifference curves of investors. We propose safety first criteria and get optimal portfolio model under this criteria. Two methods are given to do with probability condition, and we obtain optimal portfolio. At last, we give safety first index to portfolio performance management.     

Liquidity Risk Management of the Open-end Securities Investment Fund

The main object of this paper is to research the liquidity risk management of the open-end securities investment fund in line with the real position of China's securities market and investment regulation of the open-end securities investment fund.So the paper concentrates on discussing the redemption forecasting methods,stock liquidity assessment system,portfolio selection in line with the redemption forecast,and financing from the other institution,which are the main parts of liquidity risk management of the open-end securities investment fund.     

非线性方程最优拟合的缩张算法

本文提出一种可实现非线性方程最优拟合的新方法－缩张算法（Ｃ－Ｅ算法）。该算法由若干循环组成,每一循环都包含收缩和扩张两个步骤。因而,可以在多维起始空间的内、外漫游搜索目标函数,并利用搜索过程所反馈的信息调整搜索中心和步长;通过较少次Ｃ－Ｅ循环的搜索,便能逼近给定非线性方程的最适参数值。该算法不需要给出方程的导数或偏导数,减少了计算的复杂性,也可能推广应用于解决其它目标函数的最优化问题。     

Financial Risk Measurement: CVaR

The precise measurement to risks is principal for the effective risk management,both major in theory and practice.Value-at-Risk,a widely accepted risk measure,has some deadly deficiencies.The authors introduce a new risk measure,Conditional-Value-at-Risk,which comes into being based on the VaR measure. They introduce CVaR's definition and the risk-measuring model on it and also its applications in portfolio management,comparatively with VaR measure.     

田间肥效试验数据的频率分析和施肥决策

为解决农业试验统计分析软件、扬州分析器(2.2)、Excel进行回归分析建立的部分非典型性肥料效应方程推荐的施肥量出现异常偏大、偏低甚至负值,脱离当地生产实际的问题。本文应用概率理论的基本知识和频数的原理和方法,对油菜田间肥效试验数据应用频率分析法进行统计分析,得到的油菜优化施肥量产量为1732.4 kg/hm²,氮、磷、钾优化组合范围分别为210.36~149.64 kg/hm²、81.89~58.11 kg/hm²、81.89~58.11 kg/hm²,与试验地（田）和当地生产实际相吻合。本研究是在频率分析的基础上,用加权平均方法,确定各种不同产量目标的生产因素组合,将其中产量高,出现频率大（稳产）,用肥节省的组合作为优化生产措施,具有增加施肥决策信息量,减少或避免小概率事件的风险的优点。可解决肥效试验数据分析统计汇总,应用扬州分析器(2.2)、Excel、DPS等统计分析软件进行回归分析建立的部分非典型肥料效应函数推荐的施肥量和目标产量出现异常值,与当地生产实际不相符的问题。肥料效应函数方程经方差分析不显著的试验,能否应用该研究方法进行施肥决策,推荐氮、磷、钾肥料优化组合和优化施肥量产量,还需在以后的工作实践中进一步探讨。     

A Class of Exact Solution for RLW-Burgers Equation

A class of analytic solution for RLW Burgers equation and KdV Burgers equation are given which include results of some papers.These solutions can be expressed as some linear combination of solutions of Burgers equation and RLW equation or KdV equation which correct conclusion in some paper.     

Two Formulas of Debt Valuation About risky Enterprise with Contingent Claims Analysis and Comparison

Risky debt valuation differs greatly from that of no risk so that under uncertainty of income flower and discount rate, usually we can not get a kind of resonlution to express the type. With no account of the discount rate, we are absorbed in property value influence under uncertainty. As generalizing the theory of option pricing, contingent claims analysis can handel debt valuation, and sometime give closed form expressions.Two formula obtained by Merton and Black&Cox, are Compared and different conditions are discussed. At last, some comment on formula of debt valuation is given.     

Contingent Claims Analysis of Valuation of Risky Debt with Bankruptcy Costs

Research on valuation of corporate risky debt is given when bankruptcy costs are taken into account. Bankruptcy costs are expenditures of enterprise that get into bankruptcy, as a result, enterprise asset value is reduced, and debt value is reduced too because bondholders only receive asset value deducted from bankruptcy costs. Differential equation which risky debt value follows is given and a model about infinite maturity debt is obtained. By applying contingent claims pricing and stochastic calculus methods, the paper derives a risky debt value formula, this formula can illustrate the effect of investment policy and dividend policy on risky debt value. At last the results are comporred with results of Merton and Black and it is found that our results improve Merton and Black's.     

Option-pricing of Completeness Market and the Choice of Hedging-trade Strategies

This article is based on the existence of an arbitrage about a portfolio in an disequilbrium market under the supposition of the stochastic market. The authors defined the T option priee equilibrium price, and illuminated these definitions at first. With the knowledge of stochastic analysis, it is demonstrated that the price of European put option equals its callo ption. They both equal equilibrium price. In addition, under the same supposition, it is discussed that the choice of hedging trade planning, got the formula of hedging trading.A example to show how to use the formula.     

Change of the Interest Rate of Loan When CommercialBanks Become More Risk Averse

Through the equation of balance sheet between assessment and debt, this paper reformulates the function with two stochastic process of credit risk and interest rate risk under the full consideration of the profile of the losses of bad debts of the commercial banks, deduces the function of loan rate under the maximum utility of profit margin of commercial banks. The Beyer's estimation is used to analyse the changes of the loan rate when the extent of the risk averse of commercial banks. The risk averse extent is raised from the Arrow-Pratt risk averse to Ross risk averse. It is pointed out that the more risk averse of a commercial bank, the even higher the interest rate the bank charges to its borrower.     

Image denoising based on adaptive graph regularization

Adaptive regularization can select different parameters based on the features of local areas in an image, which can differentiate the edges and noise in an image flexibly. An adaptive graph regularization is proposed based on graph spectral theory and adaptive regularization, which uses the Non local means to generate the weighting function of graph. The adaptive graph regularization equation is used to filter the noisy image. Simulation results show that the proposed method can effectively remove the noise and is superior to other graph theory based partial differential equation methods.     

VaR Model and Application to Securities Investment Management

VaR model is one of methods to measure and control market risk.This paper analyzes VaR model principle and its main factors.According to function relation,the relationship between the portfolio value and its market risk factors are sorted in two kinds: linear and nonlinear.The method of calculating the VaR is put forward.Finally,the article analyzes the application of VaR model to portfolio,risk control,information disclosure and financial supervison.