• 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.7
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• pp.771-779
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• 2004

Unsteady behavior of the early wake in the viscous flow field past an impulsively started semicircular cylinder is studied numerically. In this paper, we propose the hybrid diffusion scheme to simulate dynamic characteristics of wake such as a fishtail-like flapping and an alternate vortex-shedding more accurately. This diffusion scheme based on particle strength exchange is mixed with the stochastic nature of random walk method. Also, the viscous splitting algorithm which calculates convective and diffusion terms successively is applied in order to handle random walk method effectively. Consequently, the early behavior of wake due to the breakdown of symmetrical vortici balance is more practically simulated with the vortex particle method.

• Journal of the Korean Statistical Society
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• v.29 no.4
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• pp.489-499
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• 2000

We propose a new instrumental variable estimator of the complex parameter of a class of univariate complex-valued diffusion processes defined by the possibly non-stationary and/or nonlinear stochastic differential equations. On the basis of the exact finite sample distribution of the pivotal quantity, we construct the exact confidence intervals and the exact tests for the parameter. Monte-Carlo simulation suggests that the new estimator seems to provide a viable alternative to the maximum likelihood estimator (MLE) for nonlinear and/or non-stationary processes.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.385-408
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• 2001

This is an introduction to a stochastic version of E. Cartan′s symplectic mechanics. A class of time-symmetric("Bernstein") diffusion processes is used to deform stochastically the exterior derivative of the Poincare-Cartan one-form on the extended phase space. The resulting symplectic tow-form is shown to contain the (a.e.) dynamical laws of the diffusions. This can be regarded as a geometrization of Feynman′s path integral approach to quantum theory; when Planck′s constant reduce to zero, we recover Cartan′s mechanics. The underlying strategy is the one of "Euclidean Quantum Mechanics".

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1311-1325
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• 2011

In this paper the Milstein method is proposed to approximate the solution of a linear stochastic differential equation with Poisson-driven jumps. The strong Milstein method and the weak Milstein method are shown to capture the mean square stability of the system. Furthermore using some technique, our result shows that these two kinds of Milstein methods can well reproduce the stochastically asymptotical stability of the system for all sufficiently small time-steps. Some numerical experiments are given to demonstrate the conclusions.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.295-305
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• 2014

Yan & Hanson [8] and Makate & Sattayatham [6] extended Bates' model to the stochastic volatility model with jumps in both the stock price and the variance processes. As the solution processes of finding the characteristic function, they sought such a function f satisfying $$f({\ell},{\nu},t;k,T)=exp\;(g({\tau})+{\nu}h({\tau})+ix{\ell})$$. We add the term of order ${\nu}^{1/2}$ to the exponent in the above equation and seek the explicit solution of f.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.11-31
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• 2023

The paper presents a critical analysis of selected topics related to the modeling of interacting species in which prey has nonlinear reproduction, which is in competition with predator. The mathematical model's stochastic stability is investigated. The method of designing appropriate Lyapunov functions is used to identify permanence conditions among the parameters of the model and conditions for the structure to no longer be extinct. The system's two-dimensional diffusive stability is regarded and studied. The system experiences the process of saddle-node bifurcation by varying the death rate of predator parameter. Further effects of parameters that undergo inherent oscillations are numerically investigated, revealing that as the intensity of predation parameter b is increased, the device encounters non-periodic and damped oscillations.

• Computers and Concrete
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• v.32 no.3
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• pp.247-261
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• 2023

Due to the non-uniform distribution of meso-structure, the diffusion of chloride ions in concrete show the characteristics of characteristics of randomness and fuzziness, which leads to the non-uniform distribution of chloride ions and the non-uniform corrosion of steel rebar in concrete. This phenomenon is supposed as the main reason causing the uncertainty of the bearing capacity deterioration of reinforced concrete structures. In order to analyze and predict the durability of reinforced concrete structures under chloride environment, the random features of chloride ions transport in concrete were studied in this research from in situ meso-structure of concrete. Based on X-ray CT technology, the spatial distribution of coarse aggregates and pores were recognized and extracted from a cylinder concrete specimen. In considering the influence of ITZ, the in situ mesostructure of concrete specimen was reconstructed to conduct a numerical simulation on the diffusion of chloride ions in concrete, which was verified through electronic microprobe technology. Then a stochastic study was performed to investigate the distribution of chloride ions concentration in space and time. The research indicates that the influence of coarse aggregate on chloride ions diffusion is the synthetic action of tortuosity and ITZ effect. The spatial distribution of coarse aggregates and pores is the main reason leading to the non-uniform distribution of chloride ions both in spatial and time scale. The chloride ions concentration under a certain time and the time under a certain concentration both satisfy the Lognormal distribution, which are accepted by Kolmogorov-Smirnov test and Chi-square test. This research provides an efficient method for obtain mass stochastic data from limited but representative samples, which lays a solid foundation for the investigation on the service properties of reinforced concrete structures.

• The Korean Journal of Financial Management
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• v.20 no.1
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• pp.213-231
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• 2003

This paper uses the Efficient Method of Moments(EMM) of Gallant and Tauchen to estimate continuous-time stochastic volatility diffusion model for the Korean Composite Stock Price Index, sampled daily over $1995\sim2002$. The estimates display non-normality of stock index return, leptokurtic distribution, and stochastic volatility. Funker, this study suggests that two factor stochastic volatility model will be more desirable than one factor stochastic volatility model to estimate daily Korean stock return and also suggests that the stochastic volatility diffusions should allow for Poisson jumps of time-varying intensity.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.381-393
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• 2005

We consider a type of large deviation principle obtained by Freidlin and Wentzell for the solution of Stochastic differential equations in a conuclear space. We are using exponential tail estimates and exit probability of a Ito process. The nuclear structure of the state space is also used.