• Proceedings of the Korean Geotechical Society Conference
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• 1998.05a
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• pp.35-81
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• 1998

Distinct Element Method(DEM) has a great advantage to model the discontinuous behaviour of jointed rock masses such as rotation, sliding, and separation of rock blocks. Geometrical data of joints by a field monitoring is not enough to model the jointed rock mass though the results of DE analysis for the jointed rock mass is most sensitive to the distributional properties of joints. Also, it is important to use a properly joint law in evaluating the stability of a jointed rock mass because the joint is considered as the contact between blocks in DEM. In this study, a stochastic modelling technique is developed and the dilatant rock joint is numerically modelled in order to consider th geometrical and mechanical properties of joints in DE analysis. The stochastic modelling technique provides a assemblage of rock blocks by reproducing the joint distribution from insufficient joint data. Numerical Modelling of joint dilatancy in a edge-edge contact of DEM enable to consider not only mechanical properties but also various boundary conditions of joint. Preprocess Procedure for a stochastic DE model is composed of a statistical process of raw data of joints, a joint generation, and a block boundary generation. This stochastic DE model is used to analyze the effect of deviations of geometrical joint parameters on .the behaviour of jointed rock masses. This modelling method may be one tool for the consistency of DE analysis because it keeps the objectivity of the numerical model. In the joint constitutive law with a dilatancy, the normal and shear behaviour of a joint are fully coupled due to dilatation. It is easy to quantify the input Parameters used in the joint law from laboratory tests. The boundary effect on the behaviour of a joint is verified from shear tests under CNL and CNS using the numerical model of a single joint. The numerical model developed is applied to jointed rock masses to evaluate the effect of joint dilation on tunnel stability.

• The Korean Journal of Financial Management
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• v.24 no.4
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• pp.1-43
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• 2007

The traditional Black-Scholes model for option pricing is based on the assumption that the log-return of the underlying asset follows a Brownian motion. But this assumption has been criticized for being unrealistic. Thus, for the last 20 years, many attempts have been made to adopt different stochastic processes to derive new option pricing models. The option pricing models based on L$\acute{e}$vy processes are being actively studied originating from the Gerber-Shiu model driven by H. U. Gerber and E. S. W. Shiu in 1994. In 2004, G. H. L. Cheang derived an option pricing model under multiple L$\acute{e}$vy processes, enabling us to adopt drift and jumps to the Gerber-Shiu model, while Gerber and Shiu derived their model under one L$\acute{e}$vy process. We derive the Gerber-Shiu model which includes drift and jumps under L$\acute{e}$vy processes. By adopting a Gamma distribution, we expand the Heston model which was driven in 1993 to include jumps. Then, using KOSPI200 index option data, we analyze the price-fitting performance of our model compared to that of the Black-Scholes model. It shows that our model shows a better price-fitting performance.