• Communications for Statistical Applications and Methods
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• v.20 no.6
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• pp.475-480
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• 2013

The surplus process in a risk model is stochastically analyzed. We obtain the characteristic function of the level of the surplus at a finite time, by establishing and solving an integro-differential equation for the distribution function of the surplus. The characteristic function of the stationary distribution of the surplus is also obtained by assuming that an investment of the surplus is made to other business when the surplus reaches a sufficient level. As a consequence, we obtain the first and second moments of the surplus both at a finite time and in an infinite horizon (in the long-run).

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.229-235
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• 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
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• v.23 no.5
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• pp.423-432
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• 2016

In this paper, we stochastically analyze the continuous time surplus process in a risk model which involves a continuous type investment. It is assumed that the investment of the surplus to other business is continuously made at a constant rate, while the surplus process stays over a given sufficient level. We obtain the stationary distribution of the surplus level and/or its moment generating function by forming martingales from the surplus process and applying the optional sampling theorem to the martingales and/or by establishing and solving an integro-differential equation for the distribution function of the surplus level.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.915-920
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• 2014

We consider a continuous time surplus process with investments the sizes of which are independent and identically distributed. It is assumed that an investment of the surplus to other business is made, if and only if the surplus reaches a given sufficient level. We establish an integro-differential equation for the distribution function of the surplus and solve the equation to obtain the moment generating function for the stationary distribution of the surplus. As a consequence, we obtain the first and second moments of the level of the surplus in an infinite horizon.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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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.

• 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.

• Journal of Technology Innovation
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• v.13 no.1
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• pp.295-315
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• 2005

The mobile telecommunication service industry plays major role of the realization to the perfect information society in the 21st century and has a great influence in society and culture. The government has enticed the mobile company to keep up to make the mobile service fee low. In this situation, this paper estimates consumer surplus and price elasticity with on-line survey data from the consumer of mobile service. The total estimated consumer surplus of the market is reached to 6.43trillion won. The consumer surplus from SKT is estimated to 4.98trillion won and 1.66trillion won and 0.67trillion won was made by KTF and LGT respectively. The result also shows that consumer surplus is expected to be increased by the increase of the mobile service demand and the sales.

• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.95-103
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• 2015

We introduce a surplus process which follows a diffusion process with positive drift and is subject to two types of claim. We assume that type I claim occurs more frequently, however, its size is stochastically smaller than type II claim. We obtain the ruin probability that the level of the surplus becomes negative, and then, decompose the ruin probability into three parts, two 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, when the sizes of both types of claim are exponentially distributed, to compare the impacts of two types of claim on the ruin probability of the surplus along with that of the diffusion process.

• KDI Journal of Economic Policy
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• v.40 no.3
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• pp.69-89
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• 2018

We study whether a default option attached to non-recourse mortgages improves borrowers' surplus from mortgage financing. By defaulting on mortgage debt, borrowers can save their non-collateralized income from being foreclosed. In exchange, borrowers must forgo non-monetary surplus from retaining any collateral. Banks may charge a high mortgage rate due to increased default rates. We find that the interest rate of non-recourse mortgage decreases with the borrower's surplus from home ownership. Moreover, non-recourse mortgages benefit only borrowers who deem housing property as an investment asset. Hence, the transition to a non-recourse mortgage is detrimental to welfare if the borrower enjoys a large surplus from home ownership. Although the borrower privately knows how much surplus she enjoys from home ownership, a menu of non-recourse mortgage contracts may exist, yielding a separating equilibrium without information rent.

• Journal of the Korean Institute of Educational Facilities
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• v.15 no.6
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• pp.30-38
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• 2008

The aim of this study is to investigate present situation about occurrence of surplus classrooms by the merger and abolition of rural elementary schools, and to deduce basic architectural data for efficient utilization. It was examined based on the analysis of using pattern and interview of teachers of modernized elementary model schools. The occurrence ratio of surplus classrooms was about 30 to 60 percentages among seven investigated schools, the ratio was gradually increasing. Most of them were nearly leaving without certain practical use because of inaccessibility and low degree of diversion. The characteristic about diversion of surplus classroom was shown to change from special or learning room to living-related room and management-related room in order, finally, it was used a room for child care with a lapse of time. Long-tenn and continuous data accumulation for diversion and utilization of surplus classroom should be required.