• 한국경영과학회지
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• 제13권2호
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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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• 제16권2호
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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.

• 한국정보과학회논문지:시스템및이론
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• 제34권2호
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• pp.65-72
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• 2007

임베디드 시스템의 신인도(Dependability)를 높이기 위해 기존 컴퓨터시스템에서 주로 사용되는 결함허용(Fault-tolerant) 기법을 그대로 적용시키는 것은 임베디드 시스템의 엄격한 비용 제약과 설치공간 부족 등을 고려할 때 적합하지 않다. 본 논문에서는 각 시스템 구성요소(Component)들의 여분(Redundancy)을 최소한도로 사용하는 임베디드 시스템에 적합한 소프트웨어 결함허용 기법을 제안한다. 이를 위하여 임베디드 시스템의 신인도를 반영하기 위한 기준인 유용도(Utility) 척도를 정의하고, 실제 시스템의 결함허용을 위해 각각의 시스템 구성요소들의 재구성(Reconfiguration) 조합에 대한 유용도 평가를 수행하였다. 이러한 유용도 평가는 일반적으로는 지수복잡성(Exponential Complexity)을 가지게 되나, 본 논문에서는 각각의 구성요소에 대한 소프트웨어 수준의 계층적 그룹화 개념을 이용하여 복잡도를 크게 감소시켰다. 이를 통해 임베디드 시스템의 일부 부품에 결함이 발생했을 시, 시스템의 고장(Failure)을 방지 할 수 있도록 전체 시스템 단계에서 가능한 최대 유용도를 제공하는 구성조합으로의 재구성 작업을 가능하게 하였다.

• East Asian mathematical journal
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• 제27권1호
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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.

• 대한산업공학회지
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• 제7권1호
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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.

• 충청수학회지
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• 제29권1호
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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.

• 대한수학회보
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• 제56권6호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2001년도 추계학술대회 논문집
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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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• 제27권3_4호
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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.

• 대한교통학회지
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• 제27권4호
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• pp.127-135
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• 2009

도로 주행중 제공된 교통정보는 운전자의 단기기억에 저장되고 이는 수초가 지나면 기억에서 사라진다. 정보제공의 효과 평가시 더미변수를 이용하는 기존방법으로는 이러한 현상을 반영할 수 없는 한계가 있다. 보다 적절한 평가를 위해서, 본 연구는 전방 시야가 제약된 도심 신호교차로 접근로에서 실시한 주행실험 자료를 토대로 운전자의 단기기억을 고려한 차내 교통안전정보의 효용함수 특성화와 안전도 평가방법론을 제안한다. 이를 위해서, 운전자의 속도선택에 기초한 주행 안정성 평가모형을 순서 프로빗모형으로 개발하고, 교통운영, 기하구조, 도로환경, 운전자 요소를 동시에 고려하여 차내 교통안전정보의 효용함수를 추정하였다. 분석결과, 본 연구에서 제안한 차내 교통안전정보의 효용을 설명하는데 정규밀도 함수(지수함수)가 적합하고, 효용은 약 22초 동안 유지되며, 크기는 시간증가에 따라 감소하는 것으로 나타났다. 또한, 차내 실시간 교통안전정보의 중요도는 교통운영요소 보다는 낮고 기하구조요소 보다는 높은 것으로 분석되었다.