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SINGULAR INTEGRAL EQUATIONS AND UNDERDETERMINED SYSTEMS
KIM, SEKI 한국산업정보응용수학회 1998 한국산업정보응용수학회 Vol.2 No.2
In this paper the linear algebraic system obtained from a singular integral equation with variable coefficients by a quadrature-collocation method is considered. We study this underdetennined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1,1] can be shown under some assumptions on the coefficients of the equation.
Kim, Tae Hyun,Yang, Yoon Mee,Han, Chang Yeob,Koo, Ja Hyun,Oh, Hyunhee,Kim, Su Sung,You, Byoung Hoon,Choi, Young Hee,Park, Tae-Sik,Lee, Chang Ho,Kurose, Hitoshi,Noureddin, Mazen,Seki, Ekihiro,Wan, Yu-J American Society for Clinical Investigation 2018 The Journal of clinical investigation Vol.128 No.12
ON THE USE OF REALIZED QUASI-MONTE CARLO METHOD IN EUROPEAN OPTION PRICING
Seki Kim,Doobae Jeon 한국산업응용수학회 2006 한국산업응용수학회 학술대회 논문집 Vol.1 No.2
The pricing of options is a very important problem encountered in complex financial markets. The famous Black-Scholes model provides explicit closed form solutions for the values of European call and put options. But for many other options, either there are no closed form solutions, or if such closed form solution exist, the formulas exhibiting them are complicated and difficult to evaluate accurately by conventional methods. In this case, Monte Carlo methods may prove to be valuable. Monte Carlo methods are often used when other methods are difficult to implement due to the complexity of the problem. The disadvantages of Monte Carlo Methods are that the error term is probability and that it can be computationally burdensome to achieve a high level of accuracy. Quasi-Monte Carlo is technique for improving the efficiency of the Monte Carlo Method. Under the conventional approach pseudo-random numbers yields an error bound that is probabilistic which can be a disadvantage. Another drawback of the standard approach is that many simulations may be required to obtain a high level of accuracy. Quasi-Monte Carlo Methods use sequences that are deterministic instead of random. These sequences improve convergence and give rise to deterministic error bounds. But these Methods have some limits which does not reflect the trend of rise, fall and hold. We divide 2-dimensional space into three parts. Each three parts indicate rise, fall and hold. If this trend apply to the Quasi-Monte Carlo Methods, it may be better than the known Methods.
THE DISCRETE SLOAN ITERATE FOR CAUCHY SINGULAR INTEGRAL EQUATIONS
KIM, SEKI 한국산업정보응용수학회 1998 한국산업정보응용수학회 Vol.2 No.2
The superconvergence of the Sloan iterate obtained from a Galerkin method for the a p proximate solution of the singular integral equation based on the use of two sets of orthogonal polynomials is investigated. The discrete Sloan iterate using Gaussian quadrature to evaluate the integrals in the equation becomes the Nystro¨m approximation obtained by the same rules. Consequently, it is impossible to expect the faster convergence of the Sloan iterate than the discrete Galerkin approximation in practice.
HEDGING OPTION PORTFOLIOS WITH TRANSACTION COSTS AND BANDWIDTH
KIM, SEKI 한국산업정보응용수학회 2000 한국산업정보응용수학회 Vol.4 No.2
Black-Scholes equation arising from option pricing in the presence of cost in trading the underlying asset is derived. The transaction cost is chosen precisely and generalized to reflect the trade in the real world. Furthermore the concept of the bandwidth is introduced to obtain the better rehedging. The model with bandwidth derived in this paper can be used to calculate the more accurate option price numerically even if it is nonlinear and more complicated than the models shown before.