• 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.

• Korean Management Science Review
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• v.25 no.3
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• pp.1-12
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• 2008

The Swaption is one of the popular Interest rates derivatives. In spite of such a popularity, the swaption pricing formula is hard to derived within the theoretical consistency. Most of swaption pricing model are heavily depending on the simulation technique. We present a new class of swaption model based on the multi-factor HJM levy-mixture model. A key contribution of this paper is to provide a generalized swaption pricing formula encompassing many market stylize facts. We provide an approximated closed form solution of the swaption price using the Gram-Charlier expansion. Specifically, the solution form is similar to the market models, since our approximation is based on the Lognormal distribution. It can be directly compared with the traditional Black's formula when the size of third and fourth moments are not so large. The proposed extended levy model is also expected to be capable of producing the volatility smiles and skewness.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.1-19
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• 1999

In this paper we establish some limit theorems for a two-parameter fractional Levy Brownian motion on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter fractional Levy Brownian motion.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.207-224
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• 1998

After the review of known results on the connections between selfsimilar processes with independent increments (processes of class L) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bound sets. Comparison in transience-recurrence of the Levy process and the process of class L associated with a common distribution of class L is made.

• Journal of Families and Better Life
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• v.20 no.5
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• pp.69-85
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• 2002

The purpose of this study was to develop a scheme to standardize apartment management expenses levy. I have conducted theoretical research on the literature for the foundation of this study. I have also surveyed many different kinds of levies with help from several apartment complex managers in Busan as well as the executive secretaries of Busan Citizen's Coalition for Economic Justice. I held 30 meetings with the experts in this process to discuss the standardization of the levy. The finalized scheme for standardization is in line with the Act for Management of Multiple Family Housing. Because description of the whole standardized scheme is too lengthy for one article, I decided to present it in three parts. This article is the first part of the series. The remaining two parts will be published in future issues.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.825-834
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• 2002

Poisson processes are widely used in reliability and survival analysis. In particular, multiple event time data in survival analysis are routinely analyzed by use of Poisson processes. In this paper, we consider large sample properties of nonparametric Bayesian models for Poisson processes. We prove that the posterior distribution of the cumulative intensity function of Poisson processes is consistent under regularity conditions on priors which are Levy processes.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.139-157
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• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2012.05a
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• pp.436-442
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• 2012

In the process of liquid rocket engine design, obtaining method of the dynamic characteristics of engine should be emphasized typically to determine the control logic and algorithms of the throttle valves in the propellant feed pipeline. However, determining the dynamic characteristics of an engine through the autonomous test is very hard and laborious, so that the numerical approach is prevailing. In this study, using the previously developed dynamic analysis model of the engine around the steady state, we introduced a disturbance to this model, and obtained the dynamic response in the time domain. And by applying the well-known Levy method to this temporal response, we could deduce the transfer function of that system that can give us various information of engine and can be manipulated to design the control system.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.351-368
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• 2014

This study presents a hunting search based optimum design algorithm for engineering optimization problems. Hunting search algorithm is an optimum design method inspired by group hunting of animals such as wolves, lions, and dolphins. Each of these hunters employs hunting in a different way. However, they are common in that all of them search for a prey in a group. Hunters encircle the prey and the ring of siege is tightened gradually until it is caught. Hunting search algorithm is employed for the automation of optimum design process, during which the design variables are selected for the minimum objective function value controlled by the design restrictions. Three different examples, namely welded beam, cellular beam and moment resisting steel frame are selected as numerical design problems and solved for the optimum solution. Each example differs in the following ways: Unlike welded beam design problem having continuous design variables, steel frame and cellular beam design problems include discrete design variables. Moreover, while the cellular beam is designed under the provisions of BS 5960, LRFD-AISC (Load and Resistant Factor Design-American Institute of Steel Construction) is considered for the formulation of moment resisting steel frame. Levy Flights is adapted to the simple hunting search algorithm for better search. For comparison, same design examples are also solved by using some other well-known search methods in the literature. Results reveal that hunting search shows good performance in finding optimum solutions for each design problem.