• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.287-297
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• 2022

In this paper, we consider a risk-minimization hedging problem for a special European contingent claims. The existence and uniqueness of strategy are given constructively. Firstly, a non-standard European contingent is demonstrated as stochastic payment streams. Then the existence of the risk minimization strategy and also the uniqueness are proved under two kinds market information by using Galtchouk-Kunita-Watanabe decomposition and constructing a 0-achieving strategy risk-minimizing strategies in full information. And further, we have proven risk-minimizing strategies exists and is unique under restrict information by constructing a weakly mean-selffinancing strategy.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1073-1086
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• 2009

This paper considers the problems of martingale measures and risk-minimizing hedging strategies in the market with restricted information. By constructing a general restricted information market model, the explicit relation of arbitrage and the minimal martingale measure between two different information markets are discussed. Also a link among all equivalent martingale measures under restricted information market is given. As an example of restricted information markets, this paper constitutes a jump-diffusion process model and presents a risk minimizing problem under different information. Through $It\hat{o}$ formula and projection results in Schweizer[13], the explicit optimal strategy for different market information are given.

• Journal of the Korean Operations Research and Management Science Society
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• v.29 no.2
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• pp.45-57
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• 2004

The purpose of this paper is studying the valuation of option prices in Incomplete markets. A market is said to be incomplete if the given traded assets are insufficient to hedge a contingent claim. This situation occurs, for example, when the underlying stock process follows jump-diffusion processes. Due to the jump part, it is impossible to construct a hedging portfolio with stocks and riskless assets. Contrary to the case of a complete market in which only one equivalent martingale measure exists, there are infinite numbers of equivalent martingale measures in an incomplete market. Our research here is focusing on risk minimizing hedging strategy and its associated minimal martingale measure under the jump-diffusion processes. Based on this risk minimizing hedging strategy, we characterize the dynamics of a risky asset and derive the valuation formula for an option price. The main contribution of this paper is to obtain an analytical formula for a European option price under the jump-diffusion processes using the minimal martingale measure.

• Journal of the Korean Physical Society
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• v.73 no.10
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• pp.1577-1583
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• 2018

Tumor-treating fields therapy involves placing pads onto the patient's skin to create a low- intensity (1 - 3 V/cm), intermediate frequency (100 - 300 kHz), alternating electric field to treat cancerous tumors. This new treatment modality has been approved by the Food and Drug Administration in the USA to treat patients with both newly diagnosed and recurrent glioblastoma. To deliver the prescribed electric field intensity to the tumor while minimizing exposure of organs at risk, we developed an optimization method for the electric field distribution in the body and compared the electric field distribution in the body before and after application of this optimization algorithm. To determine the electric field distribution in the body before optimization, we applied the same electric potential to all pairs of electric pads located on opposite sides of models. We subsequently adjusted the intensity of the electric field to each pair of pads to optimize the electric field distribution in the body, resulting in the prescribed electric field intensity to the tumor while minimizing electric fields at organs at risk. A comparison of the electric field distribution within the body before and after optimization showed that application of the optimization algorithm delivered a therapeutically effective electric field to the tumor while minimizing the average and the maximum field strength applied to organs at risk. Use of this optimization algorithm when planning tumor-treating fields therapy should maintain or increase the intensity of the electric field applied to the tumor while minimizing the intensity of the electric field applied to organs at risk. This would enhance the effectiveness of tumor-treating fields therapy while reducing dangerous side effects.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.179-192
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• 2012

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maximization problem is used and we get the same results as in the paper [21].

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.363-381
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• 2012

Shortfall risk is considered by taking some exposed risks because the superhedging price is too expensive to be used in practice. Minimizing shortfall risk can be reduced to the problem of finding a randomized test ${\psi}$ in the static problem. The optimization problem can be solved via the classical Neyman-Pearson theory, and can be also explained in terms of hypothesis testing. We introduce the classical Neyman-Pearson lemma expressed in terms of mathematics and see how it is applied to shortfall risk in finance.

• Journal of Information Technology Applications and Management
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• v.14 no.3
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• pp.95-113
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• 2007

To minimize IT operational risks and the opportunity cost for lost business hours. it is necessary to have preparedness in advance and mitigation activities for minimization of a loss due to the business discontinuity. There are few cases that banks have a policy on systematic management, system recovery and protection activities against system failure. and most developers and system administrators response based on their experience and the instinct. This article focuses on the mitigation model development for minimizing the incidents of disk unit in IT operational risks. The model will be represented by a network model which is composed of the three items as following: (1) the risk factors(causes, attributes and indicators) of IT operational risk. (2) a periodic time interval through an analysis of historical data. (3) an index or an operational regulations related to the examination of causes of an operational risk. This article will be helpful when enterprise needs to hierarchically analyze risk factors from various fields of IT(information security, information telecommunication, web application servers and so on) and develop a mitigation model. and it will also contribute to the reduction of operational risks on information systems.

• The Journal of the Korean dental association
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• v.42 no.6 s.421
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• pp.392-397
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• 2004

• The Journal of the Korean dental association
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• v.42 no.6 s.421
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• pp.398-403
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• 2004

• Journal of the Korea Safety Management & Science
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• v.9 no.2
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• pp.123-134
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• 2007

This paper focuses on the in-house reliability assurance plan for the bulk materials of each company. The reliability assurance needs in essence a long time and high cost for testing the materials. In order to reduce the time and cost, accelerated life test is adopted. The bulk sampling technique was used for acceptance. Design parameters might be total sample size(segments and increments}, stress level and so on. We focus on deciding the sample size by minimizing the asymptotic variance of test statistics as well as satisfying the consumer's risk. In bulk sampling, we also induce the sample size by adapting the normal life time distribution model when the variable of the lognormal life time distribution is transformed and adapted to the model. In addition, the sample size for both the segments and increments can be induced by minimizing the asymptotic variance of test statistics of the segments and increments with consumer's risk met. We can assure the reliability of the mean life and B100p life time of the bulk materials by using the calculated minimum sample size.