• 대한수학회보
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• 제54권2호
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• pp.573-581
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• 2017

Reflected Ornstein-Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. In this work, we are concerned with the study of asymptotic behaviours of parametric estimation for ergodic reflected Ornstein-Uhlenbeck processes with two-sided barriers. Moreover, we also focus on the relations between regulators and the local time process.

• 대한수학회보
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• 제56권6호
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• pp.1467-1483
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• 2019

This paper analyzes a robust optimal reinsurance and investment strategy for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and insists on seeking robust optimal strategies. The AAI's surplus process is assumed to follow a jump-diffusion model, and he is allowed to purchase proportional reinsurance or acquire new business, meanwhile invest his surplus in a risk-free asset and a risky-asset, whose price is described by an Ornstein-Uhlenbeck process. Under the criterion for maximizing the expected exponential utility of terminal wealth, robust optimal strategy and value function are derived by applying the stochastic dynamic programming approach. Serval numerical examples are given to illustrate the impact of model parameters on the robust optimal strategies and the loss utility function from ignoring the model uncertainty.

• Communications for Statistical Applications and Methods
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• 제18권2호
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• pp.229-236
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• 2011

A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general L$\'{e}$vy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential ${\alpha}$-mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.

• Journal of the Korean Statistical Society
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• 제34권4호
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• pp.281-295
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• 2005

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.879-889
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• 2004

This paper gives an approximation to the distribution function of the .rst passage time of stock price when volatility of stock price is modeled by a function of Ornstein-Uhlenbeck process. It also shows how to obtain the error of the approximation.

• 응용통계연구
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• 제31권6호
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• pp.801-810
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• 2018

확산은 금융이나 물리적 현상의 모형화에 이용되는 확률과정이다. 반복적으로 관측된 확산과정에 대하여 통계적인 모형을 구축할 때, 확률효과를 고려할 필요가 있다. 이 연구에서는 Ornstein-Uhlenbeck 확산모형과 geometric Brownian motion 확산모형에 대하여 확률효과를 도입한다. 모형모수에 대한 최도우도추정법을 적용하기 위하여, 확률효과에 대한 적절한 분포를 가정하여 닫힌 형태로 우도함수를 얻는 방법을 탐색하였다. 1991년부터 2017년까지 27년간 일일 단위로 기록된 다우존스 산업지수에 대하여 확률효과 모형을 적용하였다.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.753-763
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• 2002

When there is one change-point in the hazard rate model, a change-point estimator with the partial score process is suggested and compared with the previously developed estimators. The limiting distribution of the partial score process we used is a function of the Brownian bridge. Simulation study gives the comparison of change-point estimators.

• Communications for Statistical Applications and Methods
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• 제15권3호
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• pp.421-427
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• 2008

This paper deals with the problem of testing for the existence of change in mean and estimating the change-point when the data are from the exponential distributions. The likelihood ratio test statistic and Gombay and Horvath (1990) test statistic are compared in a power study when there exists one change-point in the exponential means. Also the change-point estimator using the likelihood ratio and the change-point estimators based on Gombay and Horvath (1990) statistic are compared for their detecting capability via simulation.

• Communications for Statistical Applications and Methods
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• 제14권2호
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• pp.443-457
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• 2007

This paper deals with the problem of testing the existence of change in mean and estimating the change-point using nonparametric bootstrap technique. A test statistic using Gombay and Horvath (1990)'s functional form is applied to derive a test statistic and nonparametric change-point estimator with bootstrapping idea. Achieved significance level of the test is calculated for the proposed test to show the evidence against the null hypothesis. MSE and percentiles of the bootstrap change-point estimators are given to show the distribution of the proposed estimator in simulation.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.511-518
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• 2009

We consider the problem of testing for change and estimating the unknown change-point in a sequence of time-ordered observations from the binomial and Poisson distributions. Including the likelihood ratio test, Gombay and Horvath (1990) tests are studied and the proposed change-point estimator is derived from their test statistic. A power study of tests and a comparison study of change-point estimators are done via simulation.