• East Asian mathematical journal
• /
• v.37 no.5
• /
• pp.553-566
• /
• 2021

In the over-the-counter market, option's buyers could have a problem for default risk caused by option's writers. In addition, many participants try to maximize their benefits obviously in investing the financial derivatives. Taking all these circumstances into consideration, we deal with the vulnerable power options under a constant elasticity variance (CEV) model. We derive an analytic pricing formula for the vulnerable power option by using the asymptotic analysis, and then we verify that the analytic formula can be obtained accurately by comparing our solution with Monte-Carlo price. Finally, we examine the effect of CEV on the option price based on the derived solution.

• Coupled systems mechanics
• /
• v.10 no.1
• /
• pp.79-102
• /
• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• Water for future
• /
• v.16 no.2
• /
• pp.123-129
• /
• 1983

One of the techniques to determine flood stages in natural channel is to find the solution of unsteady flow equations such as continuity and momentum equations. Since the exact analytic solution of these equations are not Known, the implicit numerical scheme is widely accepted tool for the approximate solution of equations. This technique is applied to the downstream of Daechung Dam in Geum River for the determination of flood stage for given frequency. However the flood stages are greatly affected by the method of reservoir Operation Method and Technical Operation Reservoir Method. Obviously, the Tech. ROM is found to be superior to Auto ROM.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.31 no.6
• /
• pp.36-44
• /
• 2003

In this paper, an analytic solution method is proposed to overcome the numerical problems when the slewing dynamics of hybrid coordinate systems is investigated via time finite element analysis. It is shown that the dynamics of the hybrid coordinate systems is governed by the coupled dual differential equations for both slewing and structural modes. Structural modes are transformed into the time-based modal coordinates and analytic spatial propagation equations are derived for each space-dependent time mode. Slew angle history is obtained analytically by appropriate applications of the boundary conditions and structural propagation is re-calculated using the slew angle. Numerical examples are demonstrated to validate the proposed analytic method in comparison to the existing state transition matrix method.

• Journal of Institute of Control, Robotics and Systems
• /
• v.7 no.10
• /
• pp.867-873
• /
• 2001

The purpose of this study is to find analytic solution of determining the optimal capacity (lot-size) of multiproduct acyclic multistage production and inventory system to meet the finished product demand under the constraint of finite intermediate storage. Intermediate storage is a practical way to mitigate the material flow imbalance through the line of supply and demand chain. However, the cost of constructing and operating storage facilities is becoming substantial because of increasing land value, environmental and safety concern. Therefore, reasonable decision-making about the capacity of processes and storage units is an important subject for industries. The industrial solution for this subject is to use the classical economic lot sizing method, EOQ/EPQ(Economic Order Quantity/Economic Production Quantity) model, incorporated with practical experience. But EOQ/EPQ model is not suitable for the chemical plant design with highly interlinked processes and storage units because it is developed based on single product and single stage. This study overcomes the limitation of the classical lot sizing method. The superstructure of the plant consists of the network of serially and/or parallelly interlinked non-continuous processes and storage units. The processes transform a set of feedstock materials into another set of products with constant conversion factors. A novel production and inventory analysis method, PSW(Periodic Square Wave) model, is applied to describe the detail material flows among equipments. The objective function of this study is minimizing the total cost composed of setup and inventory holding cost. The advantage of PSW model comes from the fact that the model provides a set of simple analytic solutions in spite of realistic description of the material flows between processes and storage units. the resulting simple analytic solution can greatly enhance the proper and quick investment decision for the preliminary plant design problem confronted with economic situation.

• Journal of the Korea Society for Simulation
• /
• v.28 no.3
• /
• pp.49-56
• /
• 2019

In this paper, we deal with two pricing of bond options using the relationship between the forward rate model and the Libor rate model. First, we derive a formula for obtaining discounted bond prices using the restrictive condition of the Ritchken and Sankarasubramanian (RS), and then use the volatility function relationship of the forward rate and the Libor rate models to find the analytic solution (AS) of bond options pricing. Second, the price of the bond options is calculated by simulating several scenarios from the presented condition using Monte Carlo Simulation (MCS). Comparing the results of the implementation of the above two pricing methods, the relative error (RE) is obtained, which means the ratio of AS and MCS. From the results, we can confirm that the RE is around 3.9%, which means that the price of the bond options can be predicted very accurately using the MCS as well as AS.

• Journal of Soil and Groundwater Environment
• /
• v.13 no.2
• /
• pp.54-61
• /
• 2008

The drawdown distribution due to pumping by horizontal or slanted wells is analyzed by numerical modelling. In the numerical modelling uses 1-D discrete element feature included in commercial groundwater modeling program FEFLOW (version 5.1) and the results are compared with the semi analytic solution which uses superposition of successive point sources proposed by Zhan and Zlotnik (2002). Results of the numerical modeling agree well with the semi analytic solution except for very near field region of sink sources. The drawdown distribution due to pumping in riverbank filtration(RBF) plan site can be evaluated quantitatively by the numerical modeling in this study.

• Journal of Mechanical Science and Technology
• /
• v.20 no.12
• /
• pp.2230-2241
• /
• 2006

This paper presents a sole application of boundary element method to the conjugate heat transfer problem of thermally developing laminar flow in a thick walled pipe when the fluid velocities are fully developed. Due to the coupled mechanism of heat conduction in the solid region and heat convection in the fluid region, two separate solutions in the solid and fluid regions are sought to match the solid-fluid interface continuity condition. In this method, the dual reciprocity boundary element method (DRBEM) with the axial direction marching scheme is used to solve the heat convection problem and the conventional boundary element method (BEM) of axisymmetric model is applied to solve the heat conduction problem. An iterative and numerically stable BEM solution algorithm is presented, which uses the coupled interface conditions explicitly instead of uncoupled conditions. Both the local convective heat transfer coefficient at solid-fluid interface and the local mean fluid temperature are initially guessed and updated as the unknown interface thermal conditions in the iterative solution procedure. Two examples imposing uniform temperature and heat flux boundary conditions are tested in thermally developing region and compared with analytic solutions where available. The benchmark test results are shown to be in good agreement with the analytic solutions for both examples with different boundary conditions.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.22 no.3
• /
• pp.113-143
• /
• 1997

Most of the conflict problems between 2 persons can be represented as a bi-matrix game, because player's utilities, in general, are non-zero sum and change according to the progress of game. In the bi-matrix game the equilibrium point set which satisfies the Pareto optimality can be a good bargaining or coordination solution. Under the condition of incomplete information about the risk attitudes of the players, the bargaining or coordination solution depends on additional elements, namely, the players' methods of making inferences when they reach a node in the extensive form of the game that is off the equilibrium path. So the investigation about the players' inference type and its effects on the solution is essential. In addition to that, the effect of an individual's aversion to risk on various solutions in conflict problems, as expressed in his (her) utility function, must be considered. Those kinds of incomplete information make decision maker Bayesian, since it is often impossible to get correct information for building a decision making model. In Baysian point of view, this paper represents an analytic frame for guessing and learning opponent's attitude to risk for getting better reward. As an example for that analytic frame. 2 persons'bi-matrix game is considered. This example explains that a bi-matrix game can be transformed into a kind of matrix game through the players' implicitly cooperative attitude and the need of arbitration.

• Journal of Mechanical Science and Technology
• /
• v.18 no.2
• /
• pp.221-229
• /
• 2004

In this work, an elastic-plastic stress analysis has been conducted for silicon carbide fiber reinforced magnesium metal matrix composite beam. The composite beam has a rectangular cross section. The beam is cantilevered and is loaded by a single force at its free end. In solution, the composite beam is assumed perfectly plastic to simplify the investigation. An analytical solution is presented for the elastic-plastic regions. In order to verify the analytic solution results were compared with the finite element method. An rectangular element with nine nodes has been choosen. Composite plate is meshed into 48 elements and 228 nodes with simply supported and in-plane loading condations. Predictions of the stress distributions of the beam using finite elements were overall in good agreement with analytic values. Stress distributions of the composite beam are calculated with respect to its fiber orientation. Orientation angles of the fiber are chosen as $0^{circ},\;30^{circ},\;45^{circ},\;60^{circ}\;and\;90^{circ}$. The plastic zone expands more at the upper side of the composite beam than at the lower side for $30^{circ},\;45^{circ}\;and\;60^{circ}$ orientation angles. Residual stress components of ${\sigma}_{x}\;and \;{\tau}_{xy}$ are also found in the section of the composite beam.