• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.397-406
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• 2013

We present an improved binomial method for pricing European- and American-type Asian options based on the arithmetic average of the prices of the underlying asset. At each node of the tree we propose a simple algorithm to choose the representative averages among all the effective averages. Then the backward valuation process and the interpolation are performed to compute the price of the option. The simulation results for European and American Asian options show that the proposed method gives much more accurate price than other recent lattice methods with less computational effort.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.151-160
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• 2011

Typically, it is hard to find a closed form solution of option pricing formula under an asset governed by a change point process. In this paper we derive a closed-form solution of the valuation function for an American perpetual put option under an asset having a change point. Structural changes are formulated through a change-point process with a Markov chain. The modified smooth-fit technique is used to obtain the closed-form valuation function. We also guarantee the optimality of the solution via the proof of a corresponding verification theorem. Numerical examples are included to illustrate the results.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.745-751
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• 2002

In this paper, we Shall find the unique rational price associated with the exchange option. Also, we find the decomposition of Snell envelope and value function of the American exchange option.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.39-47
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• 2003

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7］are generalized and improved.

• School Mathematics
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• v.12 no.1
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• pp.27-43
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• 2010

In this article the conceptual meaning of expression, equation and identity used in Korean mathematics textbooks and American mathematics textbooks is compared and discussed. For this purpose definitions and examples in several mathematics textbooks which are used in Korean elementary school, the 1st grade of middle school and American middle school are investigated. It is founded out that at first there are some parts that give rise to misunderstanding and then there are differences between the Korean terminologies and their corresponding English counterparts. The definitions of expression, equation and identity are advised to examine in the view of middle mathematics curriculum.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.197-208
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• 2006

This paper deals with the exact solution of surface gravity waves in an ocean with irregular bed topography. In order to obtain water surface elevation and run-up of infra-gravity waves when the bed is either wavy or exponential, closed form solutions are obtained. Numerical computations indicate that when solitary wave or sinusoidal wave conditions are applied at the boundary, water surface elevation attains near Gaussian profile.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.237-249
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• 2004

This paper deals with existence of positive solutions of nonlinear elliptic singular boundary value problems in a ball. It is shown that results of Grandall et al. [1] and [2] follow as special cases of our results proved in this article.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.1-16
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• 2007

Some Kamenev-type oscillation criteria are obtained for a second order quasilinear damped differential equation with impulses. These criteria generalize and improve some well-known results for second order differential equations with land without impulses. In addition, new oscillation criteria are also obtained to generalize and improve known results. Two examples of applications are given to illustrate the theory.

• School Mathematics
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• v.11 no.3
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• pp.335-349
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• 2009

The purpose of this study is to explore how a mathematics teacher's beliefs about mathematics and teaching and learning and mathematics and how such beliefs are related to her knowledge manifested in her mathematics instruction. The study illustrates images of teaching practice of an American mathematics teacher in middle grades mathematics classrooms. Results suggest that the teacher seems consistent in teaching in terms of her beliefs about mathematics and learning and teaching mathematics in some degrees. In particular, the teacher's beliefs affected the ways in which mathematics teacher organized and structured her lessons.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.53-65
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• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.