• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.669-677
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• 2013

Quasi-Monte Carlo method is known to have lower convergence rate than the standard Monte Carlo method. Quasi-Monte Carlo methods are using low discrepancy sequences as quasi-random numbers. They include Halton sequence, Faure sequence, and Sobol sequence. In this article, we compared standard Monte Carlo method, quasi-Monte Carlo methods and three scrambling methods of Owen, Faure-Tezuka, Owen-Faure-Tezuka in valuation of multi-asset European call option through simulations. Moro inversion method is used in generating random numbers from normal distribution. It has been shown that three scrambling methods are superior in estimating option prices regardless of the number of assets, volatility, and correlations between assets. However, there are no big differences between them.

• Korean Journal of Mathematics
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• v.11 no.1
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• pp.65-70
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• 2003

We show that every quasi-random graph $G(n)$ with $n$ vertices and minimum degree $(1+o(1))n/2$ has diameter either 2 or 3 and that every quasi-random graph $G(n)$ with n vertices has a clique number of $o(n)$ with wide spread.

• The Journal of the Korea Contents Association
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• v.6 no.4
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• pp.63-68
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• 2006

For the almost co티am convergent series $S_n$ of independent random variables, by investigating the limiting behavior of the tail series, $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}X_i$, the rate of convergence of the series $S_n$ to a random variable S is studied in this paper. More specifically, the equivalence between the tail series weak law of large numbers and a limit law is established for a quasi-monotone decreasing sequence, thereby extending a result of Previous work to the wider class of the norming constants.

• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.563-585
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• 2008

This paper presents how to improve the efficiency and accuracy in the pricing and sensitivity evaluation for derivatives, since the need for the evaluation of complicated derivatives is increased. The Monte Carlo(MC) simulation using the quasi random number instead of pseudo random number can improve the elapsed time and accuracy for the valuation of European-type derivatives. However, the quasi MC simulation method has its limit for applying it in the multi-dimensional case such as American-type and path-dependent options due to the increased correlation between dimensions as the dimension of random numbers is increased. In order to complement this problem, we develop a modified method in which correlation values are controlled to be below a pre-specified value. Thus, this method is applicable for the pricing of either derivatives ill which underlying assets or risk factors are several or derivatives having path-dependent or early redemption property. Furthermore, we illustrate that it is important to take an appropriate grid interval for the use of finite difference method(FDM) by applying the FDM to one example of non-symmetrical butterfly spreads.

• Proceedings of the KIEE Conference
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• 1997.07d
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• pp.1481-1484
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• 1997

This paper describes a electrical tree simulation by fractal theory. Tree patterns produced by computer simulation with random numbers were studied from the point of view of fractal dimension. Tree patterns have a variety of shapes such as branch-like, bush-like, and quasi-bush-like trees. The patterns are determined by origins and probability ratio. The fractal dimensions have been measured a function of discharge number.

• Journal of the Korean Society of Combustion
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• v.5 no.2
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• pp.19-27
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• 2000

A turbulent combustion model, based on edge flame dynamics, is discussed in order to predict global extinction of turbulent flames. The model is applicable to the broken flamelet regime of turbulent combustion, in which global extinction of turbulent flame is achieved by gradual expansion of flame holes. The edge flame dynamics is the key mechanism to describe the flame hole expansion or contraction. For flames with Lewis numbers near unity, there is a $Damk{\ddot{o}}hler$ number, namely the crossover $Damk{\ddot{o}}hler$ number, at which edge flame changes its direction of propagation. The parametric region between the quasi-steady extinction condition and the edge-flame crossover condition is a metastable region, in that flames without edge can stay in their burning states while flames with edge have to retract to expand quenching holes. Using the above properties of edge flame, Hartley and Dold proposed a Lagrangian hole dynamics, which allows us to simulate transient variation of quenching holes. In their model, each stoichiometric surface is subjected to a random sequence of scalar dissipation rate compatible to the equilibrium turbulence. Then, each stoichiometric surface will evolve, according to the combustion map, dependent on the scalar dissipation rate and existence of flame edge, If all the burning surfaces are annihilated, the event can be declared as a global extinction. The consequence obtained from the above model also can be used as a subgrid model to determine local extinction occurring in a calculation grid.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.26
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• pp.111-117
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• 1992

In the stock marketing. investor needs speedy and accurate decision making for the investment. A stock exchange index provides the important index of the early of 1993 in Korea using Fuzzy Delphi Method(F. D. M) which is widely used to a mid and long range forecasting in decision making problem. In the Fuzzy Delphi method, considerably qualified experts an first requested to give their opinion seperately and without intercommunication. The forecasting data of experts consist of Triangular Fuzzy Number (T.F.N) which represents the pessimistic, moderate, and optimistic forecast of a stock exchange index. A statistical analysis and dissemblance index are then made of these subject data. These new information are then transmitted to the experts once again, and the process of reestimation is continued until the process converges to a reasonable stable forecast of stock exchange index. The goal of this research is to forecast the stock exchange index using F.D.M. in which subjective data of experts are transformed into quasi -objective data index by some statistical analysis and fuzzy operations. (a) A long range forecasting problem must be considered as an uncertain but not random problem. The direct use of fuzzy numbers and fuzzy methods seems to be more compatible and well suited. (b) The experts use their individual competency and subjectivity and this is the very reason why we propose the use of fuzzy concepts. (c) If you ask an expert the following question: Consider the forecasting of the price index of stocks in the near future. This experts wi11 certainly be more comfortable giving an answer to this question using three types of values: the maximum value, the proper value, and the minimum value rather than an answer in terms of the probability.