• 대한수학회보
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• 제33권2호
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• pp.259-265
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• 1996

The history of option valuation problem goes back to the year 1900 when Louis Bachelier deduced on option valuation formula under the assumption that the price process follows standard Brownian motion. More than 50 years later, the research for a mathematical theory of option valuation was taken up by Samuelson ([6]) and others. This work was brought into focus in the major paper by Black and Scholes ([1]) in which a complete option valuation model was derived on the assumption that the underlying price model is a geometric Brownian motion. THis paper starts with subjects developed mainly in Harrison and Kreps ([4]) and in Harrison and Pliska ([5]). The ideas established in these papers are essential for option valuation problem, and in particularfor the point of view that we take in this paper.

• Communications for Statistical Applications and Methods
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• 제11권2호
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• pp.213-225
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• 2004

A fixed-strike lookback option is an option whose payoff is determined by the maximum (or minimum) price of the underlying asset within the option's life. Under the Black-Scholes framework, the time-t price of an equity asset follows a geometric Brownian motion. Applying the method of Esscher transforms, this paper will derive explicit pricing formulas for fixed-strike lookback call and put options, respectively. In addition, this paper will show a relationship (duality property) between the pricing formulas of the call and put options. Finally, this paper will derive explicit pricing formulas for the fixed-strike lookback options when their underlying asset pays dividends continuously at a rate proportional to its price.

• 대한기계학회논문집B
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• 제28권2호
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• pp.189-198
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• 2004

We consider the problem of whether the three-dimensional checkerboard has the connectivity. For this purpose, we first consider the problem of determining the effective conductivity of a checkerboard-shaped composite material by the Brownian motion simulation method. Specifically, we use the efficient first-passage-time technique. Simulation results show that the effective conductivity of the three-dimensional checkerboard increases faster than the two-dimensional counterpart as the contrast between the phase conductivities increases. This implies that the three-dimensional checkerboard's connectivity is stronger than the two-dimensional checkerboard's and thus each phase material of the three-dimensional checkerboard is more likely to be connected than not to be connected.

• 한국수학사학회지
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• 제20권3호
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• pp.73-90
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• 2007

본 논문은 일반화된 브라운 확률과정으로 유도된 함수공간에서 정의되는 일반화된 파인만 적분과 일반화된 푸리에-파인만 변환을 소개하고, 이들의 존재정리 및 여러 가지 성질을 설명한다. 그리고 푸리에 변환과 일반화된 해석적 푸리에-파인만 변환의 유사성을 조사한다.

• 품질경영학회지
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• 제20권2호
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• pp.11-20
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• 1992

We discuss the feed back control of the on-line QC in the Taguchi method. Taguchi(1982) used the assumptions that the quality characteristics follow an uniform distribution and the Brownian motion to draw the loss function and proposed ${\Delta}/3$ or ${\Delta}$ for the initial control limit. Adams and Woodall(1989) also proposed a different procedure but using the same loss function. We propose, in this paper the new loss function under the assumption of mainly Brownian motion and compare the results with the results of the above.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권4호
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• pp.277-293
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• 2016

We develop an efficient numerical method for pricing the Derivative Linked Securities (DLS). The payoff structure of the hybrid DLS consists with a standard 2-Star step-down type ELS and the range accrual product which depends on the number of days in the coupon period that the index stay within the pre-determined range. We assume that the 2-dimensional Geometric Brownian Motion (GBM) as the model of two equities and a no-arbitrage interest model (One-factor Hull and White interest rate model) as a model for the interest rate. In this study, we employ the Monte Carlo simulation method with the Compute Unified Device Architecture (CUDA) parallel computing as the General Purpose computing on Graphic Processing Unit (GPGPU) technology for fast and efficient numerical valuation of DLS. Comparing the Monte Carlo method with single CPU computation or MPI implementation, the result of Monte Carlo simulation with CUDA parallel computing produces higher performance.

• 충청수학회지
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• 제33권1호
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• pp.165-171
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• 2020

In this paper we consider a mixed fractional Brownian motion (mfBm) with jumps. The prices of European barrier options can be evaluated by solving a partial integro-differential equation (PIDE) with variable coefficients, which is derived from the mfBm with jumps. The 2-step backward differentiation formula (BDF2 method) proposed in [6] is applied with the second-order convergence rate in the time and spatial variables. Numerical simulations are carried out to observe the convergence behaviors of the BDF2 method under the mfBm with the Kou model.

• 품질경영학회지
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• 제26권1호
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• pp.74-87
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• 1998

This study considers optimal design of accelerated life tests under constant stress using that the first passage time to cross a critical boundary through amount of accumulated degradation has an inverse Gaussian distribution when the degradation process follows to a Brownian motion with positive drift of log linear function of stress. Optimum plans for Type I censoring are derived by minimizing the asymptotic variance of estimated quantiles at the use stress. Sensitivity analyses are also conducted to see how sensitive the optimality criterion is with respect to the uncertainties involved in the guessed values.

• 대한수학회논문집
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• 제36권4호
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• pp.685-704
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• 2021

The purpose of this paper is to establish a very general Cameron-Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space C²_a,b[0, T]. The function space C_a,b[0, T] can be induced by the generalized Brownian motion process associated with continuous functions a and b. To do this we first introduce the class ${\mathcal{F}}^{a,b}_{A_1,A_2}$ of functionals on C²_a,b[0, T] which is a generalization of the Kallianpur and Bromley Fresnel class ${\mathcal{F}}_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick theorem on the product function space C²_a,b[0, T]. Finally we use our Cameron-Storvick theorem to obtain several meaningful results and examples.

• Advances in nano research
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• 제10권4호
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• pp.349-357
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• 2021

In present study, the numerical investigations are carried out for effects of suction and blowing on boundary layer slip flow of casson nano fluid along permeable stretching cylinder in an exponential manner. The modeled PDEs are changed into nonlinear ODEs through appropriate nonlinear transformations. Change in physical quantities like friction coefficient, Nusselt and Sherwood numbers with variation of the aforementioned parameters are also examined and their numerical values are listed in the form of tables. Effects of Reynold number, suction parameter, Prandtl number, Lewis number, Brownian motion parameter and thermophoresis parameter are seen graphically with temperature profile.