• 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.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.

• 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.

• The Journal of Asian Finance, Economics and Business
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• v.9 no.1
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• pp.1-11
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• 2022

The study incorporates model uncertainty into the private equity (PE) valuation model (SWY model) (Sorensen et al., 2014) to evaluate how model uncertainty distorts the leverage and valuations of PE funds. This study applies a continuous-time model to PE project valuation, modeling the LPs' goal as multiplier preferences provided by Anderson et al. (2003), and assuming that LPs' aversion to model uncertainty causes endogenous belief distortions with entropy as a measure of model discrepancies. Concerns regarding model uncertainty, according to the theoretical model, have an unclear effect on LPs' risk attitude and GPs' decision, which is based on the value of the PE asset. It also demonstrates that model uncertainty lowers the certainty-equivalent valuation of the LPs. Finally, we compare the outcomes of the Full-spanning risk model with the Non-spanned risk model, and they match the intuitive economic reasoning. The most important implication is that model uncertainty will have negative effects on the LPs' certainty-equivalent valuation but has ambiguous effects on the portfolio allocation choice of liquid wealth. Our works contribute to two literature streams. The first is the literature that models the PE funds. The second is the literature introduces model uncertainty into standard finance models.

• Management Science and Financial Engineering
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• v.19 no.1
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• pp.11-16
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• 2013

This paper derives an equilibrium asset price when there exist three kinds of traders in financial market: a risk-averse informed trader, noise traders, and risk neutral market makers. This paper is an extended version of Kyle's (1985, Econometrica) continuous time model by introducing insider's risk aversion. We obtain not only the equilibrium asset pricing and market depth parameter but also insider's value function and optimal insider's trading strategy explicitly. The comparative static shows that the market depth (the reciprocal of market pressure) increases with time and volatility of noise traders' trading.

• Journal of Information Technology Services
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• v.12 no.4
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• pp.205-218
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• 2013

Recently, due to the proliferation of smartphones, users of mobile banking services which are based in wireless Internet without constraint of the time and places are significantly increased. In the study, considering the characteristics of mobile banking services based on the smartphone and the user behavior. we analyse the factors which have an effect on the behavioral intention to use mobile banking services based on the smartphone. For this purpose, we use the model which is based on Technology Acceptance Model (TAM) and add two constructs:the perceived enjoyment and the perceived risk. A survey data for 194 students at the K cyber university is used for statistical analysis. As a result, the perceived ease of use affects the perceived usefulness and the perceived enjoyment, and the perceived ease of use. And the perceived usefulness and perceived enjoyment affect continuous intention to use. On the other hand, the hypothesis which the perceived risk would affect adversely the continuous intention to use is rejected. Through this study, we expect to provide the useful implications for the smartphone banking services and contribute to the development of strategy for them.

• Journal of Information Technology Services
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• v.12 no.2
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• pp.243-256
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• 2013

Recently, due to the proliferation of smartphones, users of mobile multimedia services which are based on wireless internet without constraint of the time and places are significantly increased. In this study, considering the characteristics of mobile multimedia and the user behavior, we analyse the factors which have an effect on the behavioral intention to use the mobile multimedia services. For this purpose, we use the model which is based on Technology Accepted Model (TAM) and add two constructs; the perceived enjoyment and the perceived risk. A survey data for 280 students at the K cyber university is used for statistical analysis As a result, the perceived ease of use affects the perceived usefulness and the perceived enjoyment, and the perceived ease of use. And the perceived usefulness and perceived enjoyment affect continuous intention to use. On the other hand, the hypothesis which the perceived risk would affect adversely the continuous intention to use is rejected. Through this study, we expect to provide the useful implications for the mobile multimedia services and contribute to the development of strategy for them.

• 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.

• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.813-820
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• 2012

A surplus process with two types of claims is considered, where Type I claims occur more frequently, however, their sizes are smaller stochastically than Type II claims. The ruin probabilities of the surplus caused by each type of claim are obtained by establishing integro-differential equations for the ruin probabilities. The formulas of the ruin probabilities contain an infinite sum and convolutions that make the formulas hard to be applicable in practice; subsequently, we obtain explicit formulas for the ruin probabilities when the sizes of both types of claims are exponentially distributed. Finally, we show through a numerical example, that Type II claims have more impact on the ruin probability of the surplus than Type I claims.

• 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.