• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• Journal of The Korean Astronomical Society
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• v.28 no.2
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• pp.223-243
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• 1995

We describe the implementation of a multi-dimensional numerical code to solve the equations for idea! magnetohydrodynamics (MHD) in cylindrical geometry. It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. Curvature and source terms are included in a way to insure the formal accuracy of the code to be second order. The constraint of a divergence-free magnetic field is enforced exactly by adding a correction, which involves solving a Poisson equation. The Fourier Analysis and Cyclic Reduction (FACR) method is employed to solve it. Results from a set of tests show that the code handles flows in cylindrical geometry successfully and resolves strong shocks within two to four computational cells. The advantages and limitations of the code are discussed.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.6
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• pp.565-574
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• 2002

We propose an algorithm for the robust transmission of video in error prone environment based on multiple description (MD) scheme and simple rate-distortion operators. The redundancy rate-distortion (RRD) criteria is used to split a one-layer compressed video stream into two correlated descriptions. The proposed algorithm can find more candidate points on the RRD curve than the conventional RRD based methods. A new distortion measure is also defined in this paper, which considers more realistic error environments. Since the proposed MD video coder is based on the standard H.263 coder, each description can be decoded independently by the standard H.263 decoder. Also, several descriptions can be decoded into a single stream by additional merge stage and the H.263 decoder. Simulation results show that the proposed MD video coder yields better performance than the conventional MD splitting algorithm at all bitrates both in single and two description cases.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1229-1244
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• 2017

In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.

• Tuberculosis and Respiratory Diseases
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• v.86 no.3
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• pp.203-215
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• 2023

Background: Surgical resection is the standard treatment for early-stage lung cancer. Since postoperative lung function is related to mortality, predicted postoperative lung function is used to determine the treatment modality. The aim of this study was to evaluate the predictive performance of linear regression and machine learning models. Methods: We extracted data from the Clinical Data Warehouse and developed three sets: set I, the linear regression model; set II, machine learning models omitting the missing data: and set III, machine learning models imputing the missing data. Six machine learning models, the least absolute shrinkage and selection operator (LASSO), Ridge regression, ElasticNet, Random Forest, eXtreme gradient boosting (XGBoost), and the light gradient boosting machine (LightGBM) were implemented. The forced expiratory volume in 1 second measured 6 months after surgery was defined as the outcome. Five-fold cross-validation was performed for hyperparameter tuning of the machine learning models. The dataset was split into training and test datasets at a 70:30 ratio. Implementation was done after dataset splitting in set III. Predictive performance was evaluated by R² and mean squared error (MSE) in the three sets. Results: A total of 1,487 patients were included in sets I and III and 896 patients were included in set II. In set I, the R² value was 0.27 and in set II, LightGBM was the best model with the highest R² value of 0.5 and the lowest MSE of 154.95. In set III, LightGBM was the best model with the highest R² value of 0.56 and the lowest MSE of 174.07. Conclusion: The LightGBM model showed the best performance in predicting postoperative lung function.