• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.751-759
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• 2018

Cho et al. (Communications for Statistical Applications and Methods, 23, 423-432, 2016) introduced a risk model with a continuous type investment and studied the stationary distribution of the surplus process. In this paper, we extend the earlier analysis by assuming that additional instant investment is made when the surplus process reaches a certain sufficient level. We obtain the explicit form of the stationary distribution of the surplus process. The case is shown as an example, when the amount of claim is exponentially distributed.

• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.1-12
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• 2013

In this paper, we introduce a continuous-time risk model where the surplus follows a diffusion process with positive drift while being subject to two types of claims. We assume that the sizes of both types of claims are exponentially distributed and that type I claims occur more frequently, however, their sizes are smaller than type II claims. We obtain the ruin probability that the level of the surplus becomes negative, by establishing an integro-differential equation for the ruin probability. We also obtain the ruin probabilities caused by each type of claim and the probability that the level of the surplus becomes negative naturally due to the diffusion process. Finally, we illustrate a numerical example to compare the impacts of two types of claim on the ruin probability of the surplus with that of the diffusion process in the risk model.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2022.10a
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• pp.15-17
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• 2022

In order to minimize surplus parts in ball bearing selective assembly systems, it is necessary to optimize the selection probability by grasping the dimensional distribution of each part. But the use of a complex system causes delays in the production process. In this paper, we propose cluster priority selection algorithm that can quickly and simply determine the selection priority in ball bearing selective assembly system. In addition, we assume the simulated situation with the data collected in the actual ball bearing selective assembly process, and evaluate the incidence of surplus part and runtime by simulating the cluster priority selection algorithm and the exiting algorithm. As a result of the simulation, the cluster priority selection algorithm generated 83.8% less surplus parts, and 39.7% less runtime than the existing algorithm.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.81-87
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• 2012

A continuous time risk model is considered, where the premium rate is constant and the claims form a compound Poisson process. We assume that an injection is made, which is an immediate increase of the surplus up to level u > 0 (initial level), when the level of the surplus goes below ${\tau}$(0 < ${\tau}$ < u). We derive the formula of the ruin probability of the surplus by establishing an integro-differential equation and show that an explicit formula for the ruin probability can be obtained when the amounts of claims independently follow an exponential distribution.

• East Asian mathematical journal
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• v.27 no.1
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• pp.91-100
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• 2011

It is important to find an optimal strategy which maximize the surplus of the insurance company at the maturity time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy, under the CEV model, which maximizes the expected exponential utility of the final value of the surplus at T. To do this optimization problem, the corresponding Hamilton-Jacobi-Bellman equation will be transformed a linear partial differential equation by applying a Legendre transform.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.1-10
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• 2014

In this paper, we study approximations of the ruin probability in a continuous time surplus process. First, we introduce the well-known approximation formulas of the ruin probability such as Cram$\acute{e}$r, Tijms' and De Vylder's methods. We, then, suggest new approximation formulas of two types, which improve the existing approximation formulas. One is Cram$\acute{e}$r and Tijms' type which makes use of the moment generating function of distribution of a claim size and the other is De Vylder's type which makes use of the surplus process with exponential claims. Finally, we compare, by illustrating numerical examples, the newly suggested approximation formulas with the existing approximation formulas of the ruin probability.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.426-430
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• 2008

Hot shear-welding is a process of bonding two plates together by using shearing stress in a controlled manner. This study dealt with the hot shear-welding process of two aluminum plates. These two plates were piles up in the shear-welding mold. Due to the shearing stress, these two plates were cut off longitudinally, and meantime they were welded together. During this process the control of the surplus material flow is very important, and it can be realized by designing the overlapping length and the shape of the cavity. The commercial software Deform-3D was employed to predict the effect of these two factors. The overlapping length and the shape of the cavity that presents the optimum design was then developed to get a good shear-welding process.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1467-1483
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• 2019

This paper analyzes a robust optimal reinsurance and investment strategy for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and insists on seeking robust optimal strategies. The AAI's surplus process is assumed to follow a jump-diffusion model, and he is allowed to purchase proportional reinsurance or acquire new business, meanwhile invest his surplus in a risk-free asset and a risky-asset, whose price is described by an Ornstein-Uhlenbeck process. Under the criterion for maximizing the expected exponential utility of terminal wealth, robust optimal strategy and value function are derived by applying the stochastic dynamic programming approach. Serval numerical examples are given to illustrate the impact of model parameters on the robust optimal strategies and the loss utility function from ignoring the model uncertainty.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.937-942
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• 2009

In this paper, a continuous-time risk process in an insurance business is considered, where the premium rate is constant and the claim process forms a compound Poisson process. We say that a ruin occurs if the surplus of the risk process becomes negative. It is practically impossible to calculate analytically the ruin probability because the theoretical formula of the ruin probability contains the recursive convolutions and infinite sum. Hence, many authors have suggested approximation formulas of the ruin probability. We introduce a new approximation formula of the ruin probability which extends the well-known De Vylder's and exponential approximation formulas. We compare our approximation formula with the existing ones and show numerically that our approximation formula gives closer values to the true ruin probability in most cases.

• Industrial Engineering and Management Systems
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• v.8 no.3
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• pp.131-138
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• 2009

The variable sampling inspection scheme with screening for the purpose of assuring the upper limit of maximum expected surplus loss after inspection has been proposed. In this inspection scheme, it has been assumed that a product lot consists of products manufactured through a single production line and lot quality characteristics follow a normal distribution. In the previous literature with respect to inspection schemes, it has been commonly assumed that lot quality characteristics obey a single normal distribution under the condition that all products are manufactured in the same condition. On the other hand, the production line is designed in order that the workload of respective processes becomes uniform from the viewpoint of line balancing. One of the solutions for the bottleneck process is to arrange the workshops in parallel. The lot quality characteristics from such a production line with the process consisting of some parallel workshops might not follow strictly the single normal distribution. Therefore, we expand an applicable scope of the above mentioned variable sampling inspection scheme with screening in this article. Concretely, we consider the variable sampling inspection with screening for the purpose of assuring the upper limit of average outgoing surplus quality loss in the production lots when the lot quality follows the mixed normal distribution.