• Communications for Statistical Applications and Methods
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• 제25권1호
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• pp.91-97
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• 2018

In this paper, we show that there exists an optimal investment policy for the surplus in a risk model, in which the surplus is continuously invested to other business at a constant rate a > 0, whenever the level of the surplus exceeds a given threshold V > 0. We assign, to the risk model, two costs, the penalty per unit time while the level of the surplus being under V > 0 and the opportunity cost per unit time by keeping a unit amount of the surplus. After calculating the long-run average cost per unit time, we show that there exists an optimal investment rate $a^*$>0 which minimizes the long-run average cost per unit time, when the claim amount follows an exponential distribution.

• 응용통계연구
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• 제29권7호
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• pp.1165-1172
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• 2016

보험 상품의 잉여금은 보험료 수입에 의해 증가하며 고객이 보험료를 청구할 때 감소한다. 보험회사는 잉여금이 충분히 많아지면 잉여금의 일부를 재투자하는 것을 통해 이익을 창출한다. 본 연구에서는 보험료 수입과 청구를 고려하여 잉여금의 수준을 나타낸 기존의 잉여금 모형을 소개하고 기존의 모형에 재투자의 개념과 운용비용을 도입하여 장시간에 걸친 단위시간당 평균비용을 구하고, 이를 최소화하는 재투자 수준과 목표 잉여금을 구한다.

• Journal of the Korean Statistical Society
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• 제32권1호
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• pp.65-71
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• 2003

We consider the finite dam with compound Poisson inputs which is called M/G/1 finite dam. We assign some costs related to operating the dam and calculate the long-run average cost per unit time. Then, we find the optimal dam capacity under which the average costs is minimized.

• Journal of the Korean Statistical Society
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• 제26권1호
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• pp.147-154
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• 1997

An infinite dam with a compound Poisson input having exponential jumps is considered. As an output policy, we adopt the $P_{\lambda}$$^{M}$ Policy. After assigning costs to the dam we obtain the long-rum average cost per unit time of operating the dam and find the optimal values of .lambda. and M which minimize the long-run average cost.t.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1345-1352
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• 2008

An inventory with constant demand is studied. We adopt a renewal argument to obtain the transient and stationary distribution of the level of the inventory. We show that the stationary distribution can be also derived by making use of either the level crossing technique or the renewal reward theorem. After assigning several managing costs to the inventory, we calculate the long-run average cost per unit time. A numerical example is illustrated to show how we optimize the inventory.

• Journal of the Korean Data and Information Science Society
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• 제8권1호
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• pp.85-89
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• 1997

In this paper, we consider a random replacement model with minimal repair, which is a generalization of the random replacement model introduced Lee and Lee(1994). It is assumed that a system is minimally repaired when it fails and replaced only when the accumulated operating time of the system exceeds a threshold time by a supervisor who arrives at the system for inspection according to Poisson process. Assigning the corresponding cost to the system, we obtain the expected long-run average cost per unit time and find the optimum values of the threshold time and the supervisor's inspection rate which minimize the average cost.

• Journal of the Korean Data and Information Science Society
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• 제22권6호
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• pp.1089-1096
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• 2011

본 논문에서는 댐으로 물이 복합 포아송 과정을 따라 유입되고, 댐 수위가 적정수준 ${\lambda}$를 넘어서게 되면 방출률 M으로 물을 방출하는 무한 댐 모형이 고려된다. 한번 내리는 비의 양이 지수분포를 따르는 경우, 정상상태에서 댐 수위의 확률적 성질들을 구한다. 댐 운영과 관리에 관련된 여러 비용을 고려한 후, 장시간에 걸친 단위시간당 평균 비용을 구하고, 이를 최소화하는 방출률 M과 적정수준${\lambda}$가 유일하게 존재함을 보인다. MATLAB을 이용하여 수치적인 결과도 함께 보인다.

• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.773-782
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• 2004

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate $\lambda$ repairs the system only if the state of the system is below a threshold $\alpha$. After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate $\lambda$ and a unique value of threshold $\alpha$ which minimize the long-run average cost per unit time.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2004년도 추계학술대회
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• pp.33-42
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• 2004

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate $\lambda$ repairs the system only if the state of the system is below a threshold $\alpha$. After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate $\lambda$ and a unique value of threshold $\alpha$ which minimize the long-run average cost per unit time.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.725-733
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• 2005

A system subject to random shocks is considered. The shocks arrive according to a Poisson process and the amount of each shock is exponentially distributed. In this paper, a periodic inspection policy for the system is compared with a random inspection policy. After assigning several maintenance costs to the system, we calculate and compare the long-run average costs per unit time under two policies.