• 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.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.683-691
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• 2002

In a game called red and black, you can stake any amount s in your possession. Suppose your goal is 1 and your current fortune is ｆ, with 0 < f < 1. You win back your stake and as much more with probability p and lose your stake with probability, q = 1- p. Ahn(2000) considered optimum strategy for this game with the value of p less than $\frac{1}{2}$ where the house has the advantage over the player. The optimum strategy at any f when p < $\frac{1}{2}$ is to play boldly, which is to bet as much as you can. In this paper we perform the simulation study to show that the Bold strategy is optimum.

• Journal of the military operations research society of Korea
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• v.30 no.1
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• pp.70-80
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• 2004

In discrete red and black, you can stake any amount s in your possession, but the value of s takes positive integer value. Suppose your goal is N and your current fortune is f, with 0＜f＜N. You win back your stake and as much more with probability p and lose your stake with probability, q = 1-p. In this study, we consider optimum strategies for this game with the value of p greater than $\frac{1}{2}$ where the player has the advantage over the house. The optimum strategy at any f when p>$\frac{1}{2}$ is to play timidly, which is to bet 1 all the time. This is called as Timid1 strategy. In this paper, we perform the simulation study to show that the Timid1 strategy is optimum in discrete red and black when p＞\frac{1}{2}.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.475-480
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• 2000

In a game called red and black, you can stake any amount is in your possession. Suppose your goal is 1 and your current fortune is $f$, with 0$p$ and lose your stake with probability, $q$=1-$p$. In this paper, we consider optimum strategies for this game with the value of $p$ less than $^1/_2$ where the house has the advantage over the player, and with the value of $p$ greater than $^1/_2$ where the player has the advantage over the house. The optimum strategy at any $f$ when $p$<$^1/_2$ is to play boldly, which is to bet as much as you can. The optimum strategy when $p$>$^1/_2$ is to bet $f\cdot\alpha$with $\alpha$, a sufficiently small number between 0 and 1.

• Journal of the military operations research society of Korea
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• v.31 no.1
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• pp.122-129
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• 2005

In discrete red and black, you can stake any amount s in your possession, but the value of s takes positive integer value. Suppose your goal is N and your current fortune is ${\Large\;f},\;with\;O<{\Large\;f}. You win back your stake and as much more with probability p and lose your stake with probability, q=1-p. In this study, we consider optimum strategies for this game with the value of p less than ${\frac{1}{2}}$ where the house has the advantage over the player. It is shown that the optimum strategy at any ${\Large\;f}$ is the DBold strategy which is to play boldly in discrete red and black when $p<{\frac{1}{2}}$. And then, we perform the simulation study to show that this strategy, which is to bet as much as you can, is optimal in discrete case.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.147-151
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• 2001

In discrete red and black, you can stake any amount s in your possession, but the value of s takes positive integer value. Suppose your goal is N and your current fortune is f, with 0$\frac{1}{2}$ where the house has the advantage over the player, and with the value of p greater than $\frac{1}{2}$ where the player has the advantage over the house. The optimum strategy at any f when p<$\frac{1}{2}$ is to play boldly, which is to bet as much as you can. The optimum strategy when p>$\frac{1}{2}$ is to bet 1 all the time.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2007.11a
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• pp.204-208
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• 2007

보험요율 및 정책 결정의 기본이 되는 파산 확률은 계산이 매우 복잡하여 보통 근사적인 방법을 사용하게 된다. 윤복식(2007)에서는 다양한 상황에서 정확하게 파산확률을 계산할 수 있는 방법이 GPH 분포에 기초하여 제안된 바 있다. 본 연구에서는 이 방법의 타당성을 다양한 실험을 통해 검증하고. 기존의 근사적 방법들과의 비교하는 것이 목적이다. 실험을 통해 이 방법이 일상적인 상황에서 뿐 아니라 클레임 분포가 비정규적인 대재해 상황에서도 정확하게 파산확률을 계산해 주는 것을 관찰할 수 있었고, 계산시간 또한 도 매우 짧아서 실용성을 겸비함을 확인할 수 있었다 또한 이 결과를 근거로, 기초적인 관측 자료만 입력하면 중간에 분포모델 설정단계를 거치지 않고 바로 분석 결과를 얻는 접근법이 제안된다.