• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.383-398
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• 2006

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1376
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• 2019

We investigate the valuation of participating life insurance policies with default risk under a geometric regime-switching jump-diffusion process. We derive explicit formula for the Laplace transform of the price of participating contracts by solving integro-differential system and then price them by inverting Laplace transforms.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1411-1425
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• 2016

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

• Land and Housing Review
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• v.3 no.1
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• pp.59-68
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• 2012

The current land development cost price system is classified as the creating land by construction price and composition changes that occur sporadically in the process of completion at the source of the factors by incurred cost price. Housing for land cost price system is a lack of objectivity which scheme of the such a gap due to the land in accordance construction and incurred cost price system so far. Therefore, in order to increase the objectivity of costing the costing of predictable surprises should be reflected in the process. Under such a background, this study defined the effective differential ratio as the predictable, estimated them for various characteristics of each business district to reflect. For this, set the properties category of five types to attributes and making the complex category and Look-up table. Which result of model validation is showed a high reliability. Therefore, Continuous accumulation of material in the future, when them to reflect the construction cost, will contribute to the bridge the gap the construction cost between incurred them.

• Journal of Internet Computing and Services
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• v.25 no.2
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• pp.93-99
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• 2024

In this paper, we derive the Partial Differential Bond Price Equation (PDBPE) by using Ito's Lemma to determine the pricing of bond on term-structure of interest rate (TSIR) model with jump. From PDBPE, the Maclaurin series (MS) and the moment-generating function (MGF) for the exponential function are used to obtain a numerical solution (NS) of the bond prices. And an algorithm for determining bond prices using Monte Carlo Simulation (MCS) techniques is proposed, and the pricing of bond is determined through the simulation process. Comparing the results of the implementation of the above two pricing methods, the relative error (RE) is obtained, which means the ratio of NS and MCS. From the results, we can confirm that the RE is less than around 2.2%, which means that the pricing of bond can be predicted very accurately using the proposed algorithms as well as numerical analysis. Moreover, it was confirmed that the bond price obtained using the MS has a relatively smaller error than the pricing of bond obtained by using the MGF.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.3D
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• pp.477-487
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• 2011

The modified repeat-sales model is employed in this study in order to identify differentiating impacts of time-varying accessibility characteristics on housing price. The results demonstrate that accessibility measures have very differential impacts on housing price over time. The improvement of accessibility through newly built facilities and apartment complex has either increased or decreased housing price. For example, the new subway line 9 has positive impact on housing price nearby, therefore price gap between subway access area and the other parts has been increased. The impact of the wide area facilities such as shopping center and hospital are decreased because they can be used more easily by the new subway line before. However, the small service area facility such as elementary school doesn't lose their impact even though subway accessibility extremely increased. The results imply that new facilities in existing residential site can affect not only housing price but also the other facilities' impact of housing price.

• Proceedings of the Korea Contents Association Conference
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• 2012.05a
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• pp.63-64
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• 2012

차분진화 알고리즘은 Storn 과 Price에 의해 제안된 메타휴리스틱 알고리즘이다. 본 논문에서는 외판원 문제를 해결하기 위한 차분진화 알고리즘을 소개한다. 차분진화 알고리즘은 실수 문제를 위한 알고리즘이므로 외판원 문제를 해결하기 위해 난수 키 표현법을 적용한다. OR Library의 표준 외판원 문제에 적용한 결과 제안한 알고리즘은 외판원 문제 해결에 가능성이 있음을 보여주었다.

• Proceedings of the KIPE Conference
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• 2003.07a
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• pp.162-167
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• 2003

In this paper, systematization design method by analogical Interpretation which is profitable in the compatability and standardization of developed products and is useful of reducing construction time and price was introduced. Systematization design based on analogical interpretation is a method which systematizes each characteristic with mathematical description in order to make variable design parameters correspond with the terms desired. In this paper, after choosing a differential transformer as the sample for design components each characteristic was expressed mathematically by analogical interpretation and miniaturized ones were manufactured by similarity factors. The relationship between input voltages of an actual differential transformer and the model and output voltages occurred by the change of the displacements in operational axis was shown.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1501-1509
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• 2011

In this study, assume that the stock price obeys the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vasicek model. Then, the Black-Scholes partial differential equation is held by using fractional Ito formula. Finally, the pricing formulae of the barrier option are obtained by partial differential equation theory. The results of Black-Scholes model are generalized.