• Communications for Statistical Applications and Methods
• /
• 제20권5호
• /
• pp.377-385
• /
• 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 Data and Information Science Society
• /
• 제23권6호
• /
• pp.1289-1297
• /
• 2012

We consider a general compound Poisson risk model in which the premium rate is surplus dependent. We analyze the joint distribution of the surplus immediately before ruin, the deffcit at ruin and the time of ruin by solving the integro-differential equation for the Gerber-Shiu discounted penalty function.

• 응용통계연구
• /
• 제21권5호
• /
• pp.755-763
• /
• 2008

This paper approaches the problem of option pricing in an incomplete market, where the underlying asset price process follows a compound Poisson model. We assume that the price process follows a compound Poisson model under an equivalent martingale measure and it converges weakly to the Black-Scholes model. First, we express the option price as the expectation of the discounted payoff and expand it at the Black-Scholes price to obtain a pricing formula with three unknown parameters. Then we estimate those parameters using the market option data. This method can use the option data on the same stock with different expiration dates and different strike prices.

• 대한안전경영과학회:학술대회논문집
• /
• 대한안전경영과학회 2010년도 추계학술대회
• /
• pp.551-557
• /
• 2010

The research proposes the hypergeometric, binomial and Poisson yield models for defective and defect. The paper also presents the hypothesis test, confidence interval and control charts for DPU(Defect Per Unit) and DPO(Defect Per Opportunity). Especially the study considers the analysis of compound Poisson yield models using various DOU density distributions.

• Journal of the Korean Statistical Society
• /
• 제36권2호
• /
• pp.229-235
• /
• 2007

We consider a ruin model whose surplus process is formed by a compound Poisson process. If the level of surplus reaches V > 0, it is assumed that a certain amount of surplus is invested. In this paper, we apply the optional sampling theorem to the surplus process and obtain the expectation of period T, time from origin to the point where the level of surplus reaches either 0 or V. We also derive the total and average amount of surplus during T by establishing a backward differential equation.

• Communications for Statistical Applications and Methods
• /
• 제18권4호
• /
• pp.433-443
• /
• 2011

잉여금의 수준에 따라 이단계의 보험요율이 적용되는 복합 포아송 위험 모형을 고려한다. 먼저 이 위험 모형에 대응되는 이단계 서비스율의 M/G/1 대기행렬 모형을 설정하고, M/G/1 대기행렬 모형에서 작업량이 0에 도달하기 전에 과부하가 발생하는 확률을 유도한다. 이과부하 확률을 이용하여 위험모형에서 잉여금이 목표값에 도달하기 전에 파산하는 확률을 구하고, 보험 청구액이 지수분포를 따르는 경우의 파산 확률을 계산한다.

• 한국경영과학회지
• /
• 제23권3호
• /
• pp.153-168
• /
• 1998

In this study we consider a CONWIP system in which the processing times at each station follow an exponential distribution and the demands for the finished Products arrive according to a compound Poisson process. The demands that are not satisfied instantaneously are assumed to be backordered. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts at each station, the proportion of backordered demands, the average number of backordered demands and the mean waiting time of a backordered demand. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. A matrix geometric method is used to solve the subnetwork in the application of the product-form approximation method. To test the accuracy of the approximation method, the results obtained from the approximation method were compared with those obtained by simulation. Comparisons with simulation have shown that the approximate method provides fairly good results.

• 한국경영과학회지
• /
• 제24권3호
• /
• pp.109-123
• /
• 1999

Fleet sizing and empty equipment redistribution are two of the most critical problems in managing a fleet of equipment over a transportation network. Where the demand pattern followed the compound Poisson process(CPP) which can be generated one or more at a time under homogeneous Poisson process(HPP), this paper presented a mathematical model to determine control parameters of a decentralized distribution policy and fleet size in case of the pure hub-and-spoke system, a popular form of a logistics system. and validated this model by simulation. That is, where the number of demanded equipments followed geometric and binomial distributions, respectively, cost models on the pure hub-and-spoke logistics system with deterministic trans-portation times, which could be solved analytically, were established and analyzed. We also compared the deterministic case with stochastic one that the transportation time follows some probability distributions.

• 한국경영과학회:학술대회논문집
• /
• 한국경영과학회 2004년도 추계학술대회 및 정기총회
• /
• pp.8-12
• /
• 2004

In this study we consider a CONWIP system in which the processing times at each station follow a Coxian distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied are backordered according to the number of demands that exist at their arrival instants. For this system we develop an approximation method to calculate order based performance measures such as the mean time of fulfilling a customer order and the mean number o: customer orders. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. Numerical tests show that the approximation method provides fairly good estimation of the performance measures of interest.

• 한국산업융합학회 논문집
• /
• 제23권6_2호
• /
• pp.1103-1110
• /
• 2020

In this study, a segmented model with Upside-Down bathtub shaped failure intensity for a repairable system are proposed under the assumption that the occurrences of the failures of a repairable system follow the Non-Homogeneous Poisson Process. The proposed segmented model is the compound model of S-PLP and LIP (Segmented Power Law Process and Logistic Intensity Process), that fits the separate failure intensity functions on each segment of time interval. The maximum likelihood estimation is used for estimating the parameters of the S-PLP and LIP model. The case study of system A shows that the S-PLP and LIP model fits better than the other models when compared by AICc (Akaike Information Criterion corrected) and MSE (Mean Squared Error). And it also implies that the S-PLP and LIP model can be useful for explaining the failure intensities of similar systems.