Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error.

Objective To establish a new pharmacokinetic model based on stochastic differential equations and perfect the fundamental theories of traditional pharmacokinetic models.Methods Firstly,the background,basic concepts and theory of pharmacokinetics were introduced;Secondly,the basic principals of pharmacokinetic modeling and stochastic differential equations were elaborated,hereby a new pharmacokinetic model was established.Results An acceptable model structure based on stochastic differential equations was obtained,and three methods for solving stochastic differential equations were given and evaluated briefly.Conclusion The pharmacokinetic model based on stochastic differential equations could separate systematic error and measurement error,and could explain complexity and indeterminacy of pharmacokinetic process better.

In order to protect brokers from customer defaults in a volatile market, an active margin system is proposed for the transactions of margin lending in China. The probability of negative return under the condition that collaterals are liquidated in a falling market is used to measure the risk associated with margin loans, and a recursive algorithm is proposed to calculate this probability under a Markov chain model. The optimal maintenance margin ratio can be given under the constraint of the proposed risk measurement for a specified amount of initial margin. An example of such a margin system is constructed and applied to $26,800$ margin loans of 134 stocks traded on the Shanghai Stock Exchange. The empirical results indicate that the proposed method is an operational method for brokers to set margin system with a clearly specified target of risk control.

Nonlinear stochastic differential equation models with unobservable variables are now widely used in the analysis of PK/PD data. The unobservable variables are often estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable variables, and a simulation-based procedure is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error.

In this article,we investigate stochastic integrals for operator-valued processes with respect to Levy processes on Gel’fand triple EHE*.By virtue of stochastic integral with respect to cylindrical Levy process on its reproducing kernel Hilbert space,we define stochastic integral for a class of operator-valued processes with respect to E*-valued Levy process.

In many theoretical analysis and engineering application fields, fractional Brownian motions has proposed to be a valuable random excitation due to its' key self-similarity and fractal nature. And Hilbert-Huang transformation is counted as an effective tool to deal with nonlinear and non-stationary data. In this paper, we propose Hilbert-Huang transformation to process fractional data, then by verifying and differentiating the marginal spectrum or power spectrum of fractional data we formulate a stochastic detection scheme.

In the Ito formula and the property Ito integral,the Moment's the general form of Brownian motion and geometric Brownian motion can be represented;In addition,the method can be applied to compute other diffusion processes' moment.

In the Ito formula and the property Ito integral,the Moment's the general form of Brownian motion and geometric Brownian motion can be represented;In addition,the method can be applied to compute other diffusion processes' moment.

In this paper, we construct a class of infinitely divisible distributions on Gel′fand triple. Based on this construction, we define Lévy processes on Gel′fand triple and give their Lévy–Itô decompositions. Then, we construct the general Lévy white noises on Gel′fand triple. By using the Riemann–Liouville fractional integral method, we define the general fractional Lévy noises on Gel′fand triple and investigate their distribution properties.

Three kinds of confidence intervals based on bootstrap method were introduced and used in the VaR evaluation of financial capital.Bootstrap method overcomes many defects of parametric method and history simulation methodl.In this paper VaR of The Shanghai Composite Index was calculated,both point estimator and confidence interval were given.By comparing those methods,some significant results were found.

Parametric method for assessing individual bioequivalence (IBE) may concentrate on the hypothesis that the PK responses are normal. Nonparametric method for evaluating IBE would be bootstrap method. In 2001, the United States Food and Drug Administration (FDA) proposed a draft guidance. The purpose of this article is to evaluate the IBE between test drug and reference drug by bootstrap and Bayesian bootstrap method. We study the power of bootstrap test procedures and the parametric test procedures in FDA (2001). We find that the Bayesian bootstrap method is the most excellent.

文章首先分析了风险投资的特性,即风险投资不是一次性完成的,而是分阶段进行的。针对这一特点,将整个风险投资决策的过程分为为多个阶段,采用多阶段实物期权分析方法,利用复合期权来评估风险投资项目的价值。通过案例分析可知,与没有考虑期权价值的项目相比,考虑期权价值的项目价值要大得多,收益率也要高得多。

The true probability of a European call option to achieve positive return is investigated under the Black-Scholes model. It is found that the probability is determined by those market factors appearing in the BS formula, besides the growth rate of stock price. Our numerical investigations indicate that the biases of BS formula is correlated with the growth rate of stock price. An alternative method to price European call option is proposed, which adopts an equilibrium argument to determine option price through the probability of positive return. It is found that the BS values are on average larger than the values of proposed method for out-of-the-money options, and smaller than the values of proposed method for in-the-money options. A typical smile shape of implied volatility is also observed in our numerical investigation. These theoretical observations are similar to the empirical anomalies of BS values, which indicates that the proposed valuation method may have some merit.

文章首先对空间统计、格点空间模型进行了简介。然后试图通过地理加权回归分析,来判断与结石娃娃病例存在显著相关的因子,得到了相关因子后,疾病控制部门可以有针对性的采取措施,并预防其他新的疾病的爆发。此模型中较重要的是空间权重矩阵,文章的相关结果利用MATLAB软件计算得到。

In this paper,by virtue of the fractional differential-integral operator and stochastic integration with respect to the fractional Lévy process on Gel'fand triple,we give an innovational representation formula of the fractional Lévy process which can be viewed as a way to transform the complicated fractional Lévy process on Gel'fand triple into a simpler Lévy process on Gel'fand triple and this formula can be applied in detecting signals and behavioral finance.

In this paper, we investigate the long-range dependence of fractional Lévy processes on Gel’fand triple and construct stochastic integral with respect to fractional Lévy processes for a class of deterministic integrands.

This paper discusses the mechanism design problem for discrete and continuous agent types under symmetric information and adverse selection separately,some important conclusions have been drawn: the effort that the insurer demands of the most efficient agent is the same under adverse selection as symmetric information and pays more under adverse selection. However,from all other agents,the insurer demands less effort and pays less under adverse selection than symmetric information.

On condition of the venture capital project product pricing process is mixed process,applying the real option analysis methods,this paper has deduced the SDE of the venture capital project option.On basis of reference [5],this paper also provides the solution to the SDE.All of these show us a train of thought for evaluation of venture capital project.

The new option on education annuity insurance introduced by [1] gives the holder the right to buy an education annuity insurance at the predetermined price when the insurant has the offer to a university.Based on [1],in this paper we introduce installment option on education annuity insurance where the holder peoridically decides whether to keep the option alive or not(by paying the installment) and we find that this option is more convenient for lower-income family to invest for children's education.In this paper,we apply binomial method and backward method to pricing the installment option.

The purpose of this article is studying the evaluation of convertible bond (CB) in Levy setting. We demonstrate that the CB call pricing can be converted to American put pricing. An approximation of CB call under double exponential jump diffusion model is given.