• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.2
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• pp.66-71
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• 1988

Let B be present value of some sequence. This paper concerns the maximization of the expected utility of the present value B when the utility function is exponential.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.145-156
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• 2008

When we consider a life insurance company that sells a large number of continuous T-year term life insurance policies, it is important to find an optimal strategy which maximizes the surplus of the insurance company at time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy which maximizes the expected exponential utility of the final value of the surplus at the end of T-th year. To do this we solve the corresponding Hamilton-Jacobi-Bellman equation.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.2
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• pp.65-72
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• 2007

As embedded system has strict cost and space constraints, it is impossible to apply conventional fault-tolerant techniques directly for increasing the dependability of embedded system. In this paper, we propose software fault-tolerant mechanism which requires only minimum redundancy of system component. We define an utility metric that reflects the dependability of each embedded system component, and then measure the defined utility of each reconfiguration combinations to provide fault tolerance. The proposed utility evaluation process shows exponential complexity. However we reduce the complexity by hierachical subgrouping at the software level of each component. When some components of embedded system are tailed, reconfiguration operation changes the system state from current faulty state to pre-calculated one which has maximum utility combination.

• East Asian mathematical journal
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• v.27 no.1
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• pp.91-100
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• 2011

It is important to find an optimal strategy which maximize the surplus of the insurance company at the maturity time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy, under the CEV model, which maximizes the expected exponential utility of the final value of the surplus at T. To do this optimization problem, the corresponding Hamilton-Jacobi-Bellman equation will be transformed a linear partial differential equation by applying a Legendre transform.

• Journal of Korean Institute of Industrial Engineers
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• v.7 no.1
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• pp.21-31
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• 1981

This paper develops a short term forecasting model for household electric power consumption in Seoul, which can be used for the effective planning and control of utility management. The model developed is based on exponentially weighted moving average model and incorporates monthly average temperature as an exogeneous factor so as to enhance its forecasting accuracy. The model is empirically compared with the Winters' three parameter model which is widely used in practice and the Box-Jenkins model known to be one of the most accurate short term forecasting techniques. The result indicates that the developed hybrid exponential model is better in terms of accuracy measured by average forecast error, mean squared error, and autocorrelated error.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.73-82
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• 2016

The utility of exponential generating functions is that they are relevant for combinatorial problems involving sets and subsets. Sequences of polynomials play a fundamental role in applied mathematics, such sequences can be described using the exponential generating functions. The actuarial polynomials ${\alpha}^{({\beta})}_n(x)$, n = 0, 1, 2, ${\cdots}$, which was suggested by Toscano, have the following exponential generating function: $${\limits\sum^{\infty}_{n=0}}{\frac{{\alpha}^{({\beta})}_n(x)}{n!}}t^n={\exp}({\beta}t+x(1-e^t))$$. A linear functional on polynomial space can be identified with a formal power series. The set of formal power series is usually given the structure of an algebra under formal addition and multiplication. This algebra structure, the additive part of which agree with the vector space structure on the space of linear functionals, which is transferred from the space of the linear functionals. The algebra so obtained is called the umbral algebra, and the umbral calculus is the study of this algebra. In this paper, we investigate some umbral representations in the actuarial polynomials.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1467-1483
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• 2019

This paper analyzes a robust optimal reinsurance and investment strategy for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and insists on seeking robust optimal strategies. The AAI's surplus process is assumed to follow a jump-diffusion model, and he is allowed to purchase proportional reinsurance or acquire new business, meanwhile invest his surplus in a risk-free asset and a risky-asset, whose price is described by an Ornstein-Uhlenbeck process. Under the criterion for maximizing the expected exponential utility of terminal wealth, robust optimal strategy and value function are derived by applying the stochastic dynamic programming approach. Serval numerical examples are given to illustrate the impact of model parameters on the robust optimal strategies and the loss utility function from ignoring the model uncertainty.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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• pp.157-160
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• 2001

Firms pursue new business opportunities for growth. Market development strategy is one of the growth strategies, which develops new market segments with current products. However, new market generally has high uncertainty, or high risk. Firms should consider the risk in making and implementing the market development strategy. In this paper, an optimal marketing resource allocation model is developed, taking into account the risk attitude of a firm in market development. Under the assumption of exponential utility function, the global optimal solution is derived, and the implications are provided.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.591-601
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• 2009

In the present paper, one new generalized 'useful' information generating function and two new relative 'useful' information generating functions have been defined with their particular and limiting cases. It is interesting to note that differentiations of these information generating functions at t=0 or t=1 give some known and unknown generalized measures of useful information and 'useful' relative information. The information generating functions facilitates to compute various measures and that has been illustrated by applying these information generating functions for Uniform, Geometric and Exponential probability distributions.

• Journal of Korean Society of Transportation
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• v.27 no.4
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• pp.127-135
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• 2009

Most traffic information that drivers receive while driving are stored in their short-term memory and disappear within a few seconds. Contemporary modeling approaches using a dummy variable can't fully explain this phenomenon. As such, this study proposes to use utility functions of real-time in-vehicle traffic safety information (IVTSI), analyzing its safety impacts based on empirical data from an on-site driving experiment at signalized intersection approach with a limited visibility. For this, a driving stability evaluation model is developed based on driver's driving speed choice, applying an ordered probit model. To estimate the specified utility functions, the model simultaneously accounts for various factors, such as traffic operation, geometry, road environment, and driver's characteristics. The results show three significant facts. First, a normal density function (exponential function) is appropriate to explain the utility of IVTSI proposed under study over time. Second, the IVTSI remains in driver's short-term memory for up to nearly 22 second after provision, decreasing over time. Three, IVTSI provision appears more important than the geometry factor but less than the traffic operation factor.