• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.863-875
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• 2010

In this paper we apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer under the criterion of mean-variance. When the risk and security assets are described by the L$\acute{e}$vy processes, the closed form solutions to the maximization problem are obtained. The mean-variance efficient strategies and frontier are also given.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.139-150
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• 2007

We investigate an optimal portfolio selection problem with transaction costs when an illiquid asset pays cash dividends and there are constraints on the illiquid asset holding. We provide closed form solutions for the problem, and by using these solutions we illustrate interesting features of optimal policies.

• The Korean Journal of Financial Management
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• v.2 no.1
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• pp.55-75
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• 1986

This article is to analyse the economic efficiency of capital market, which plays a role of resource allocation in terms of financial claims such as stock and bond. It provides various contributions to the welfare theoretical aspects of modern capital market theory. The key feature that distinguishes the theory described here from traditional welfare theory is the presence of uncertainty. Securities has time dimensions and the state and outcome of the future are really uncertain. This problem resulting from this uncertainty can be solved by complete market, but it has a weak power to explain real stock market. Capital Market is faced with the uncertainity because it is a kind of incomplete market. Individuals and firms in capital market made their consumption-investment decision by their own criteria, i. e. the maximization of expected utility form intertemporal consumption and the maximization of the market value of firm. We noted that allocative decisions that had to be made in the economy could be naturally subdivided into two groups. One set of decisions concerned the allocation of first-period resources among consumption $C_i$, investment in risky firms $I_j$, and riskless investment M. The other decisions concern the distribution among individuals of income available in the second period $Y_i(\theta)$. Corresponing to this grouping, the theoretical analysis of efficiency has also been dichotomized. The optimality of the distribution of output in the second period is distributive efficiency" and the optimality of the allocation of first-period resources is 'the efficiency of investment'. We have found in the distributive efficiency that the conditions for attainability is the same as the conditions for market optimality. The necessary and sufficient conditions for attainability or market optimality is that (1) all utility functions are such that -$\frac{{U_i}^'(Y_i)}{{U_i}^"(Y_i)}={\mu}_i+{\lambda}Y_i$-linear risk tolerance function where the coefficients ${\mu}_i$ and $\lambda$ are independent of $Y_i$, and (2) there are homogeneous expectations, i. e. ${\Large f}_i(\theta)={\Large f}(\theta)$ for every i. On the other hand, the efficiency of investment has disagreement about optimal investment level. The investment level for market rule will not generally lead to Pareto-optimal allocation of investment. This suboptimality is caused by (1)the difference of Diamond's decomposable production function and mean-variance valuation model and (2) the selection of exelusive investment or competitive investment. In conclusion, this article has made an analysis of conditions and processes of Pareto-optimal allocation of resources in capital marker and tried to connect with significant issues in modern finance.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.2
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• pp.77-90
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• 2009

Total profit level Increases if a company increase the cost for achieving R&D related goals of equipment productivity enhancement, production cost saving, or for achieving equipment scale target, sales volume goal. But how much money should be invested to achieve a certain level of profit? We formulated the model to set the optimal goal levels to minimize the investment cost under the constraint that certain level of total profit should be guaranteed. This model derived from a case of P steel company. We found that this should be considered in relation with the production sales planning (known as optimal product mix problem) to guarantee the profit. We suggested a nonlinear programming model, 3 valiant form of the p+roduct mix problem. We can find the optimal Investment level for the R&D related goals or sales volume goal, equipment scale target for the P steel company using the model.

• 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 Electrical Engineering and Technology
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• v.5 no.2
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• pp.239-245
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• 2010

Today, as power trades between generators and loads are liberalized, the uncertainty level of power systems is rapidly increasing. Therefore, transmission operators are required to incorporate these uncertainties when establishing an investment plan for effective operation of transmission facilities. This paper proposes the methodology for an optimal solution of transmission expansion plans for the long-term in a deregulated power system. The proposed model uses the probabilistic cost of transmission congestion for various scenarios and the annual increasing rates of loads. The locations and the installation times of expanded transmissions lines with minimum cost are acquired by the model. To minimize the investment risk, the Mean-Variance Markowitz portfolio theory is applied to the model. In a case study, the optimal solution of a transmission expansion plan is obtained considering the uncertain power market.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.4
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• pp.560-566
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• 2008

Today, as the power trades between generation companies and power customer are liberalized, the uncertainty level of operated power system is rapidly increased. Therefore, transmission operators as decision makers for transmission expansion are required to establish a deliberate investment plan for effective operations of transmission facilities considering forecasted conditions of power system. This paper proposes the methodology for the optimal solution of transmission expansion in deregulated power system. The paper obtains the expected value of transmission congestion cost for various scenarios by using occurrence probability. In addition, the paper assumes that increasing rates of loads are the probability distribution and indicates the location of expanded transmission line, the time for transmission expansion with the minimum cost for the future by performing the Montecarlo simulation. To minimize the investment risk as the variance of the congestion cost, Mean-Variance Markowitz portfolio theory is applied to the optimization model by the penalty factor of the variance. By the case study, the optimal solution for transmission expansion plan considering the feature of market participants is obtained.

• International Journal of Quality Innovation
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• v.9 no.2
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• pp.57-77
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• 2008

The $21^{st}$ century is a new century of environmental protection. Environmental protection is one of the most important subject matters yet to come. Moreover, as the public pays more attention to environmental problems, enterprises should increase their investment in environmental management. Therefore, determining the investment level for environmental management and allocating the investment to associated environmental management activities has become a major task. The principal and agent theory and sales response functions are used for analysis in this research. The allocation of capital investment in environmental management is found to have significant impact on the aggregate sales response, aggregate profit and investment level. Therefore, in preparing the budget for environmental management, enterprises should focus on investment allocation decisions, determine the investment level and allocation method using integrated means, and apply submarket data in the allocation decision-making process. In other words, in setting the investment level, executive management should take managers' willingness into consideration. In allocating capital investment, managers should identify the optimal allocation method based on submarket characteristics.

• Journal of Digital Convergence
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• v.11 no.12
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• pp.265-274
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• 2013

The business cycle during a recession leads to negative effects on raising funds and operations management of company. In particular, the company with many inventories in the recession causes liquidity problem. Which leads to frustration in the competitive strategy management. In this case the company experiencing cash or liquidity problems attempts to reduce its investment in inventory. However, reducing inventory investment makes problems to increase inventory operating costs. This paper presents sensitivity of total cost compared to the size for reducing inventory investment. This will guarantee the relevance of the reducing inventory investment. Optimal Inventory levels also may be required to be less than the optimal levels without reduction on inventory investments.

• Asia pacific journal of information systems
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• v.21 no.4
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• pp.27-43
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• 2011

This article explores economic models that show the optimal level of information security investment in the presence of interdependent security risks, Using particular functional forms, the analysis shows that the relationship between the levels of security vulnerability and the levels of optimal security investments is affected by externalities caused by agents' correlated security risks. This article further illustrates that, compared to security investments in the situation of independent security risks, in order to maximize the expected benefits from security investments, an agent should invest a larger fraction of the expected loss from a security breach in the case of negative externalities, while an agent should spend a smaller fraction of the expected loss in the case of negative externalities.