• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.323-334
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• 2015

he current VaR model based on the J.P. Morgan's RiskMetrics structurally can not reflect the future economic situation. In this study, we propose a One-factor model resulting from the Wiener stochastic process decomposed into a systematic risk factor and an idiosyncratic risk factor. Therefore, we are able to perform a preemptive risk management by means of reflecting the predicted common risk factors in the model. Stocks in the portfolio are satisfied with the independence to each other because the common factors are fixed by the predicted value. Therefore, we can easily determine the investment in each stock to minimize the variance of the portfolio. In addition, the portfolio VaR is decomposed into the sum of the individual VaR. So we can effectively implement the constitution of the portfolio to meet the target maximum losses.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.32 no.3
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• pp.147-160
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• 2020

A stochastic probabilistic model for harbor structures such as rubble-mound breakwater has been formulated by using the generalized Wiener process considering the nonlinearity of damage drift and its nonlinear uncertainty, by which the damage path with real-time can be tracked, the residual useful lifetime at some age can also be analyzed properly. The formulated stochastic model can easily calculate the probability of failure with the passage of time through the probability density function of cumulative damage. In particular, the probability density functions of residual useful lifetime of the existing harbor structures can be derived, which can take into account the current age, its present damage state and the future damage process to be occurred. By using the maximum likelihood method and the least square method together, the involved parameters in the stochastic model can be estimated. In the calibration of the stochastic model presented in this paper, the present results are very well similar with the results of MCS about tracking of the damage paths as well as evaluating of the density functions of the cumulative damage and the residual useful lifetime. MTTF and MRL are also evaluated exactly. Meanwhile, the stochastic probabilistic model has been applied to the rubble-mound breakwater. The related parameters can be estimated by using the experimental data of the cumulative damages of armor units measured as a function of time. The theoretical results about the probability density function of cumulative damage and the probability of failure are very well agreed with MCS results such that the density functions of the cumulative damage tend to move to rightward and the amounts of its uncertainty are increased as the elapsed time goes on. Thus, the probabilities of failure with the elapsed time are also increased sharply. Finally, the behaviors of residual useful lifetime have been investigated with the elapsed age. It is concluded for rubble-mound breakwaters that the probability density functions of residual useful lifetime tends to have a longer tail in the right side rather than the left side because of the gradual increases of cumulative damage of armor units. Therefore, its MRLs are sharply decreased after some age. In this paper, the special attentions are paid to the relationship of MTTF and MRL and the elapsed age of the existing structure. In spite of that the sum of the elapsed age and MRL must be equal to MTTF deterministically, the large difference has been shown as the elapsed age is increased which is due to the uncertainty of cumulative damage to be occurred in the future.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.471-481
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• 2013

The current VaR Model based on J. P. Morgan's RiskMetrics has problem that actual loss exceeds VaR under unstable economic conditions because the current VaR Model can't re ect future economic conditions. In general, any corporation's stock price is determined by the rm's idiosyncratic factor as well as the common systematic factor that in uences all stocks in the portfolio. In this study, we propose an One-factor VaR Model for stock portfolio which is decomposed into the common systematic factor and the rm's idiosyncratic factor. We expect that the actual loss will not exceed VaR when the One-factor Model is implemented because the common systematic factor considering the future economic conditions is estimated. Also, we can allocate the stock portfolio to minimize the loss.