• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.863-875
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• 2010

In this paper we apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer under the criterion of mean-variance. When the risk and security assets are described by the L$\acute{e}$vy processes, the closed form solutions to the maximization problem are obtained. The mean-variance efficient strategies and frontier are also given.

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.100-109
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• 1983

Let ${X_i}$ be a process with stationary and independent increments whose log characteristic function is expressed as $ibut-2^{-1}\sigma^2u^2t+t\int_{{0 }^c}{(exp(iux)-1-iux(i+x^2)^{-1})dv(x)}$. Our main result is taht $x^2(\int_{\y\>x}{dv(y)})/(\int_{$\mid$y$\mid$\leqx}{y^2dv(y)+\sigma^2}) \to 1$ as $x \to 0 (resp. x \to \infty)$ is necessary, and sufficient for ${X-i}$ to have ${A_t}$ and ${B_t}$ such that $(X_t-A_t)/B_t \to^D n(0,1)$ as $t \to 0 (resp. t \to \infty)$.

• Journal of the Korean Statistical Society
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• v.17 no.1
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• pp.30-45
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• 1988

Let ${X(t) : 0 \leq t < \infty}$ be a real-valued process with stationary independent increments. In this paper, we obtain necesary and sufficint condition for there to exist a positive, nondecreasing function $\beta(t)$ so that $0 < lim sup $\mid$X(t)$\mid$/\beta(t) < \infty$ a.s. both as t tends to zero and infinity. When no such $\beta(t)$ exists we give a simple integral test for whether $lim sup $\mid$X(t)$\mid$/\beta(t)$ is zero or infinity for a given $\beta(t)$.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.26 no.5
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• pp.1-18
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• 2023

The Ecosystem Conservation Levy (formerly known as the Ecosystem Conservation Cooperation Fund) system has been in place for 20 years, and it can be said that it has now entered the settlement stage. Based on an analysis of publicly available project implementation data from 2014 to 2020, we found that: 1) As the number of return projects increases, the targets of restoration technologies are also strengthening, and it is necessary to frame a series of processes from application, creation, and monitoring for some detailed projects to improve the effectiveness and efficiency of utilizing the levy. 2) Most of the implemented projects are applied as micro-ecosystem creation, but there are many cases where the contents of the project can be seen as other project categories. This shows that the purpose of the return project needs to be approached more clearly and suggests that institutional complementation is needed from the project application stage. 3) The detailed technologies applied tend to be gradually expanding, but most of them are technologies that are not differentiated from general development projects. It is urgent to secure a more technical identity, such as a range and list of utilized technologies suitable for the characteristics and purposes of return projects. 4) It is necessary to establish a relevant evaluation system or framework to utilize the monitoring results of restoration projects. 5) There have been few cases of application of single restoration technologies since the beginning, but the content and scope of the complexity tend to expand in recent years. Even if the objectives are not comprehensive and diverse, it can be seen that many parts of the projects are oriented toward convergence, so it is necessary to conduct separate research on this. 6) As for the direction of improvement of the return project, it is possible to consider expanding the restoration and conservation focus to partially accommodate the complexity of the natural environment and human ecology. It seems that the expansion of restoration technologies that consider the role and function of humans in the natural environment should be explored.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.481-498
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• 2001

Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.

• Proceedings of the KSRS Conference
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• v.2
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• pp.1003-1006
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• 2006

Frontal regions in midlatitude storms exhibit a wide range of behavior, which can be observed by remote sensors. These include decay, strengthening, rotating, and sometimes spawning of new cyclones. Here we refine and apply recent theories of front and frontal wave development to a case of a front clearly observed and analyzed in remote sensing data. By applying innovative analysis techniques to the data we assess the respective roles of ageostrophy, background deformation, and Boundary Layer processes in determining the evolution of the surface front. Our analysis comprises of diagnosis of the terms appearing in the vorticity and divergence equations using remotely sensed observations.

• Journal of IKEEE
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• v.28 no.2
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• pp.187-198
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• 2024

Estimating the phase boundary in two-phase flow is crucial for designing and optimizing industrial processes. Electrical impedance tomography (EIT) is a promising technique for imaging phase distribution in such flows. This paper proposes using a cuckoo search (CS) optimization algorithm to estimate the phase boundary with EIT. The boundary is parameterized using the Fourier series, and the coefficients are determined by the CS algorithm. The CS algorithm iteratively seeks the phase boundary configuration by minimizing a cost function. Computer simulations and phantom experiments demonstrate the effectiveness of this method in estimating phase boundaries in two-phase flow.