• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.579-585
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• 2006

We consider a ruin model where the surplus process is formed by a Brownian motion. If the level of surplus exceeds V, then we assume that a insurer invests an amount of S to other place. In this paper, we apply martingale methods to the surplus process and obtain the expectation of period T, time from origin to the point where the level of surplus reaches either V or 0. As a consequence, we finally derive the total and average amount of surplus during T.

• 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.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1165-1172
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• 2016

In this paper, a surplus process with investments is introduced. Whenever the level of the surplus reaches a target value V > 0, amount S($0{\leq}S{\leq}V$) is invested into other business. After assigning three costs to the surplus process, a reward per unit amount of the investment, a penalty of the surplus being empty and the keeping (opportunity) cost per unit amount of the surplus per unit time, we obtain the long-run average cost per unit time to manage the surplus. We prove that there exists a unique value of S minimizing the long-run average cost per unit time for a given value of V, and also that there exists a unique value of V minimizing the long-run average cost per unit time for a given value of S. These two facts show that an optimal investment policy of the surplus exists when we manage the surplus in the long-run.

• 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.

• 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.

• The monthly packaging world
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• s.30
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• pp.80-83
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• 1995

• 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.

• The Korean Journal of Financial Studies
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• v.5 no.1
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• pp.213-236
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• 1999

최근 우리 나라는 금융환경의 변화가 진전됨에 따라 보험산업에도 변화가 일어나기 시작했다. 이에 따라 보험산업은 지급능력 및 수익성에 관심을 갖게 되었다. 이에 본 연구에서는 국내 생명보험회사의 투자수익율이 재무제표에 나타난 요인에 의해 어떻게 결정되는가를 살펴봄으로써 수익률 결정요인을 찾는데 있다. 본 연구에서 사용한 자료는 생명보험회사 33개사 중에서 외국사를 제외한 29개사를 선택하여 수집하였다. 분석 기간은 1989년부터 1996년까지이며, 생명보험회사는 기존사, 지방사, 내국사, 합작사로 구분하였다. 분석결과, 시차별 분석에서는 결정계수가 기간이 짧을수록 높게 나타났고 예측된 부호는 잉여금, 사업비율이 반대로 나타났다. 그룹별 분석에서는 기존사, 내국사, 지방사, 합작사의 모델이 각각 유의수준 5%에서 유의하였고 결정계수는 높게 나타났다. 예측부호는 자산증가율과 사업비율, 수입보험료 증가율(기존사 제외), 부채/자본비율(기존사 제외)이 일치하지 않았다. 경영평가제도에 의한 분석에서는 결정계수가 높은 편이며, 유의수준 5%에서 유의하였다. 자본증가율은 예측된 부호와 일치하나 영향력이 거의 없는 것으로 나타났다. 유동성 비율은 신설사(내국사, 지방사, 합작사)가 예측부호와 반대의 경우로 나타났다. 또한 총자산은 투자수익율과 규모에 의해 결정되지 않은 것으로 나타났다. 모집인은 투자수익율에 유의적이나 직접적인 투자요인이 아닌 것으로 분석되었다. 기존연구와 비교해 볼 때, 한국 생명보험회사의 잉여금과 효력상실 해약율은 기존연구 모형과 예측부호가 일치하나 나머지 변수는 그룹간 다소 상이하게 나타났다. 결론적으로 본 연구의 분석 결과, 예측부호는 다소 차이가 있는 것으로 나타났고, 유의적인 변수는 없는 것으로 분석된다.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.433-443
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• 2011

We consider a compound Poisson risk model in which the premiums may depend on the state of the surplus process. By using the overflow probability of the workload process in the corresponding M/G/1 queueing model, we obtain the probability that the ruin occurs before the surplus reaches a given large value in the risk model. We also examplify the ruin probability in case of exponential claims.

• 월간낙농육우
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• v.19 no.12 s.212
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• pp.101-102
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• 1999

환율이 1,000원대로 언젠가는 인하된다고 가정할때 미국과 캐나다에서 잉여 우유 수백만톤이 우리시장을 공략하려고 대기하고 있다는 것을 항상 염두해 두어야 한다. 21세기 2000원년을 맞이하면서 낙농을 하는 우리생산자는 자조금을 또 다시 조성하고 정착하는데 있어 누락자가 전혀없는 일체감을 보여줘야 할 것이다.