We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case.We suppose that the forward equation depends on some unknown finite-dimensional parameter.Th...We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case.We suppose that the forward equation depends on some unknown finite-dimensional parameter.This approximation is based on the solution of the partial differential equations and multi-step estimator-processes of the unknown parameter.As the model of observations of the forward equation we take a diffusion process with small volatility.First we establish a lower bound on the errors of all approximations and then we propose an approximation which is asymptotically efficient in the sense of this bound.The obtained results are illustrated on the example of the Black and Scholes model.展开更多
The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint ...The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.展开更多
Aiming at the solving problem of improved nonhomogeneous Poisson process( NHPP) model in engineering application,the immune clone maximum likelihood estimation( MLE)method for solving model parameters was proposed. Th...Aiming at the solving problem of improved nonhomogeneous Poisson process( NHPP) model in engineering application,the immune clone maximum likelihood estimation( MLE)method for solving model parameters was proposed. The minimum negative log-likelihood function was used as the objective function to optimize instead of using iterative method to solve complex system of equations,and the problem of parameter estimation of improved NHPP model was solved by immune clone algorithm. And the interval estimation of reliability indices was given by using fisher information matrix method and delta method. An example of failure truncated data from multiple numerical control( NC) machine tools was taken to prove the method. and the results show that the algorithm has a higher convergence rate and computational accuracy, which demonstrates the feasibility of the method.展开更多
基金This work was done with partial financial support of the RSF grant number 14-49-10079.
文摘We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case.We suppose that the forward equation depends on some unknown finite-dimensional parameter.This approximation is based on the solution of the partial differential equations and multi-step estimator-processes of the unknown parameter.As the model of observations of the forward equation we take a diffusion process with small volatility.First we establish a lower bound on the errors of all approximations and then we propose an approximation which is asymptotically efficient in the sense of this bound.The obtained results are illustrated on the example of the Black and Scholes model.
基金National Nature Science Foundation of China(No.60974030)the Chinese Universities Scientific Fund(No.CUSF-DH-D-2014059)
文摘The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.
基金National CNC Special Project,China(No.2010ZX04001-032)the Youth Science and Technology Foundation of Gansu Province,China(No.145RJYA307)
文摘Aiming at the solving problem of improved nonhomogeneous Poisson process( NHPP) model in engineering application,the immune clone maximum likelihood estimation( MLE)method for solving model parameters was proposed. The minimum negative log-likelihood function was used as the objective function to optimize instead of using iterative method to solve complex system of equations,and the problem of parameter estimation of improved NHPP model was solved by immune clone algorithm. And the interval estimation of reliability indices was given by using fisher information matrix method and delta method. An example of failure truncated data from multiple numerical control( NC) machine tools was taken to prove the method. and the results show that the algorithm has a higher convergence rate and computational accuracy, which demonstrates the feasibility of the method.
