• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.325-334
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• 2011

In this paper we consider the discrete time delayed renewal risk model. We investigate what will happen when the distribution function of the discounted proper deficit is asymptotic in the initial surplus. In doing this we establish several lemmas regarding some related ruin quantities in the discrete time delayed renewal risk model, which are of significance on their own right.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.663-669
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• 2003

This paper investigates the tail asymptotic behavior of the severity of ruin (the deficit at ruin) in the renewal model. Under the assumption that the tail probability of the claimsize is dominatedly varying, a uniform asymptotic formula for the tail probability of the deficit at ruin is obtained.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.377-385
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• 2013

We consider a compound Poisson risk model in which the premium rate changes when the surplus exceeds a threshold. The explicit form of the ruin probability for the risk model is obtained by deriving and using the overflow probability of the workload process in the corresponding M/G/1 queueing model.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.111-125
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• 2013

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.447-467
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• 2015

In this paper, we consider a multi-risk model based on the policy entrance process with n independent policies. For each policy, the entrance process of the customer is a non-homogeneous Poisson process, and the claim process is a renewal process. The loss process of the single-risk model is a random sum of stochastic processes, and the actual individual claim sizes are described as extended upper negatively dependent (EUND) structure with heavy tails. We derive precise large deviations for the loss process of the multi-risk model after giving the precise large deviations of the single-risk model. Our results extend and improve the existing results in significant ways.

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.152-152
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• 2022

Only employing historical data limits the estimation of the full distribution of probable Tropical Cyclone (TC) risk due to the insufficiency of samples. Addressing this limitation, this study introduces a semi-physical TC rainfall model that produces spatially and temporally resolved TC rainfall data to improve TC risk assessments. The model combines a statistical-based track model based on the Markov renewal process to produce synthetic TC tracks, with a physics-based model that considers the interaction between TC and the atmospheric environment to estimate TC rainfall. The simulated data from the combined model are then fitted to a probability distribution function to compute the spatially heterogeneous risk brought by landfalling TCs. The methodology is employed in South Korea as a case study to be able to implement a country-scale-based vulnerability inspection from damaging TC impacts. Results show that the proposed model can produce TC tracks that do not only follow the spatial distribution of past TCs but also reveal new paths that could be utilized to consider events outside of what has been historically observed. The model is also found to be suitable for properly estimating the total rainfall induced by landfalling TCs across various points of interest within the study area. The simulated TC rainfall data enable us to reliably estimate extreme rainfall from higher return periods that are often overlooked when only the historical data is employed. In addition, the model can properly describe the distribution of rainfall extremes that show a heterogeneous pattern throughout the study area and that vary per return period. Overall, results show that the proposed approach can be a valuable tool in providing sufficient TC rainfall samples that could be an aid in improving TC risk assessment.

• Journal of the Korean Society of Safety
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• v.33 no.1
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• pp.148-161
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• 2018

A traffic fatality by young people marked average annual decrease of 4.5% since 2011. Meanwhile, a traffic fatality by senior over 65 years old marked average annual increase of 7.9% for the last five years which means that the annual increase of traffic fatality by senior will be a serious problem. This study started questioning that senior drivers over 65 years old did not retain the same causal factor of fatal traffic accidents and thus extensively analyzed a risk of it by age group quantitatively, dividing the senior driver group into the early, middle and latter stages. Depending on the aging level, the risk of traffic fatality showed a wide difference in seven different types of traffic accidents generally, and happened to increase with latter and middle parts of the senior driver more than the early part. Therefore, this study proposes four policy suggestions: 1) The senior driver need to be offered customized driving educations and the improvement of road environment is also recommended. 2) Political assistance is needed to support and guide a safety related technology installation for the new or existing car. 3) Renewal of driving license and an aptitude test(physical examination, cognitive test) for drivers over 75 years old should take in a less than 3 years and an additional road test is needed as occasion demands. 4) Like the United States and Europe, development and extension of customized treatment guidebook for medical teams who examine senior drivers is needed and establishment of education and administration system that a supervisor of driving license renewal can impose safety restriction and American anonymity reporting system is considered to institutionalize in the medium to longer term.

• Journal of the Korean Society of Hazard Mitigation
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• v.10 no.5
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• pp.67-73
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• 2010

Relatively high density of population and buildings exists in urban area mainly because of broad job opportunities and conveniences available. In other words, if happened, there might be high possibility of disaster which can not be easily recovered. The purpose of this study is to show evaluation approach of the risk degree resulted from the disaster, which considers the attributes of urban area. Cheongju-city in Chungcheongbuk-do is selected as sample district to be estimated. The degree of overall risk including fire risk, building collapse risk, evacuation risk and gas explosion risk etc. is analyzed in the designated area. The analysis suggests the highest risk degree in Bukmun-ro district which also shows CBD decline phenomenon. Therefore, it can be not only predicted that this area as old downtown has not been provided with disaster prevention operation and urban renewal project, but also judged that administrative assistances for the disaster are required possibly soon.

• Journal of Korean Society for Quality Management
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• v.34 no.1
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• pp.40-47
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• 2006

Claim history data of rather long period were collected to assess reliability and warranty cost analyses. The data were appropriately organized to be used for further statistical analyses. For each critical component, nonparametric statistical method was applied to obtain reliability plot. Hazard plots of the components in a subsystem or system level were also obtained. Competing risk model was assumed to obtain the performance of the subsystem or system level.

• Journal of Korean Society of Water and Wastewater
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• v.27 no.3
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• pp.395-404
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• 2013

The risk of pipe-bursting in multi-regional transmission mains consisting of 89 % of singled pipeline is so high that pipeline stabilization project is required such as renewal and replacement, pipe paralleling, emergency ties. Pipeline stabilization projects could be postponed at the step of initial decision-making because effect of this project is intangible benefit like activation of economic, improvement of welfare related to water. This study is to suggest quantified economical feasibility model for intangible benefit presumption to solve above problem. Cost reduction of emergency water supply, leakage, burst restore and energy efficiency improvement was altered and applied. As a result of economic analysis taking into account estimated benefit and cost under discount rate 5.5 %, service life 40 years, sufficient economic feasibility analyzed with B/C 2.45, NPV 317,700 million won, IRR 9.09 %.