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Cheng-Hsun Wu
Department of Financial Engineering and Actuarial Mathematics, Soochow University, Taipei 215006 Taiwan

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Journal article
Published: 26 February 2021 in IEEE Transactions on Reliability
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The parallel constant-stress accelerated degradation test (PCSADT) is a popular method used to assess the reliability of highly reliable products in a timely manner. Although the maximum likelihood (ML) method is commonly utilized to estimate the PCSADT parameters, the explicit forms of the ML estimators, and their corresponding Fisher information matrix are usually difficult to obtain. In this article, we propose a two-stage ML (TSML) estimation procedure for a time-transformed model. In the proposed procedure, all the TSML estimators not only have explicit expressions but also possess consistency and asymptotic normality. Hence, this method is tractable for reliability engineers. Furthermore, the TSML estimators can provide constructive information about the unknown accelerated relationship law. The proposed method is also applied to analyze light-emitting diode data and compare the performance of our estimation procedures with the ML method via simulations.

ACS Style

Cheng-Hsun Wu; Tzong-Ru Tsai; Ming-Yung Lee. Two-Stage Maximum Likelihood Estimation Procedure for Parallel Constant-Stress Accelerated Degradation Tests. IEEE Transactions on Reliability 2021, 70, 446 -458.

AMA Style

Cheng-Hsun Wu, Tzong-Ru Tsai, Ming-Yung Lee. Two-Stage Maximum Likelihood Estimation Procedure for Parallel Constant-Stress Accelerated Degradation Tests. IEEE Transactions on Reliability. 2021; 70 (2):446-458.

Chicago/Turabian Style

Cheng-Hsun Wu; Tzong-Ru Tsai; Ming-Yung Lee. 2021. "Two-Stage Maximum Likelihood Estimation Procedure for Parallel Constant-Stress Accelerated Degradation Tests." IEEE Transactions on Reliability 70, no. 2: 446-458.

Journal article
Published: 29 December 2020 in Mathematics
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In the Black and Scholes system, the underlying asset price model follows geometric Brownian motion (GBM) with no bankruptcy risk. While GBM is a commonly used model in financial markets, bankruptcy risk should be considered in the case of a severe economic crisis, such as that caused by the COVID-19 pandemic. The omission of bankruptcy risk could considerably influence the setting of a trading strategy. In this article, we adopt an extended GBM model that considers the bankruptcy risk and study its optimal limit price problem. A limit order is a classical trading strategy for investing in stocks. First, we construct the explicit expressions of the expected discounted profit functions for sell and buy limit orders and then derive their optimal limit prices. Furthermore, via sensitivity analysis, we discuss the influence of the omission of bankruptcy risk in executing limit orders.

ACS Style

Yu-Sheng Hsu; Pei-Chun Chen; Cheng-Hsun Wu. The Optimal Limit Prices of Limit Orders under an Extended Geometric Brownian Motion with Bankruptcy Risk. Mathematics 2020, 9, 54 .

AMA Style

Yu-Sheng Hsu, Pei-Chun Chen, Cheng-Hsun Wu. The Optimal Limit Prices of Limit Orders under an Extended Geometric Brownian Motion with Bankruptcy Risk. Mathematics. 2020; 9 (1):54.

Chicago/Turabian Style

Yu-Sheng Hsu; Pei-Chun Chen; Cheng-Hsun Wu. 2020. "The Optimal Limit Prices of Limit Orders under an Extended Geometric Brownian Motion with Bankruptcy Risk." Mathematics 9, no. 1: 54.

Article
Published: 18 May 2020 in Communications in Statistics - Theory and Methods
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In order to modify the restriction that the path of the geometric Brownian motion can never reach zero, we consider an extended degradation model based on geometric Brownian motion. This model incorporates some important stochastic processes, such as geometric Brownian motion and the sinh-Gaussian process. We determine the convergence behavior of the first passage time as the random effect vanishes. The parameters of the model are estimated using the maximum likelihood method based on the first passage time observations. Both the explicit forms and the asymptotic properties of the estimators are provided. Our model can be applied to measure the brightness of LED lamps and is a reasonable extension of the original brightness model to situations in which the brightness reaches zero. The performance of the proposed model is discussed based on real data analysis and simulations.

ACS Style

Yu-Sheng Hsu; Pei-Chun Chen; Ming-Yung Lee; Cheng-Hsun Wu. Applications of an extended geometric Brownian motion degradation model. Communications in Statistics - Theory and Methods 2020, 1 -15.

AMA Style

Yu-Sheng Hsu, Pei-Chun Chen, Ming-Yung Lee, Cheng-Hsun Wu. Applications of an extended geometric Brownian motion degradation model. Communications in Statistics - Theory and Methods. 2020; ():1-15.

Chicago/Turabian Style

Yu-Sheng Hsu; Pei-Chun Chen; Ming-Yung Lee; Cheng-Hsun Wu. 2020. "Applications of an extended geometric Brownian motion degradation model." Communications in Statistics - Theory and Methods , no. : 1-15.

Journal article
Published: 02 October 2019 in Journal of Mathematical Analysis and Applications
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In the Black-Scholes system, the underlying asset price model follows a geometric Brownian motion with constant volatility and no occurrence of bankruptcy. These two characteristics contradict real financial observations. In order to agree with the nonconstant feature of the volatility and take bankruptcy risk into consideration, we modify the Black and Scholes model and propose a new model based on the efficient market hypothesis. First, we present some probability properties of the bankruptcy risk by our model and demonstrate the statistical inference for the unknown parameters. We also study the European option pricing problem and propose its statistical computation method. In addition, via a real data analysis, we show that our model captures the trend of the stock prices much better than geometric Brownian motion and clarify that the bankruptcy is a crucial factor to be considered in the Black-Scholes system.

ACS Style

Yu-Sheng Hsu; Cheng-Hsun Wu. Extended Black and Scholes model under bankruptcy risk. Journal of Mathematical Analysis and Applications 2019, 482, 123564 .

AMA Style

Yu-Sheng Hsu, Cheng-Hsun Wu. Extended Black and Scholes model under bankruptcy risk. Journal of Mathematical Analysis and Applications. 2019; 482 (2):123564.

Chicago/Turabian Style

Yu-Sheng Hsu; Cheng-Hsun Wu. 2019. "Extended Black and Scholes model under bankruptcy risk." Journal of Mathematical Analysis and Applications 482, no. 2: 123564.

Journal article
Published: 29 April 2019 in Journal of Computational and Applied Mathematics
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In this article, we derive the explicit perturbation solutions for bond-pricing equations under a multivariate Cox–Ingersoll–Ross model whose factors have weak dependences between each other. The error bounds of the perturbation approximations are demonstrated for the Riccati equation and zero-coupon bond price. These results provide the accuracy order for the perturbation approximation. Since the perturbation approximations are constructed based on the exact solution of the Riccati equation, this computational approach can be applied to deal with the stiffness problem. Numerical results are presented to show that this computation approach is tractable and accurate for evaluating the bond price.

ACS Style

Cheng-Hsun Wu. Perturbation solutions for bond-pricing equations under a multivariate CIR model with weak dependences. Journal of Computational and Applied Mathematics 2019, 361, 207 -226.

AMA Style

Cheng-Hsun Wu. Perturbation solutions for bond-pricing equations under a multivariate CIR model with weak dependences. Journal of Computational and Applied Mathematics. 2019; 361 ():207-226.

Chicago/Turabian Style

Cheng-Hsun Wu. 2019. "Perturbation solutions for bond-pricing equations under a multivariate CIR model with weak dependences." Journal of Computational and Applied Mathematics 361, no. : 207-226.