• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.121-131
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• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.293-310
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• 2007

Recently a risk measure pricing and hedging is replacing a utility-based maximization problem in the literature. In this paper, we treat the optimal problem of risk measure pricing and hedging in the friction market, i.e. in the presence of transaction costs. The risk measure pricing is also verified with the contexts in the literature.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.987-1000
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• 2011

We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where $\tilde{\psi}$ is a randomized test in the static problem. Coherent risk measure is used as risk measure in the $L^{\infty}$ random variable spaces. The paper is written in expository style to some degree. We use an average risk of measure(AVaR), which is a special coherent risk measure, to see how to hedge the modified claim in a complete market model.

• Journal of the Korea Safety Management & Science
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• v.10 no.3
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• pp.43-53
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• 2008

This study is carried out for the fire safety of the factory building, the fire risk reduction measure in compliance with an example approached in fire risk reduction systematically, contribute to reduce the fire risk. The analytical fire risk process of discovering, identifying, estimating and evaluating risk and control measure as risk reduction measures are core concept, applies loss prevention with loss control techniques. The painting process in the workplace where the fire hazard and death accident accompanies coexists. Loss prevention problem of creation prevention of dangerous atmosphere at workplace is health and human services problem of normal circumstances, must be inspected with problem of combustible gases at the time of fire explosion. Static electricity measure accomplished the risk control process thoroughly as the fire risk reduction process model with the ignition sources measure which is presented. Fire risk from within organizing will be able to classify with each field by detailedly but risk treatment process will be able to apply basically all the same concept. Consequently about risk management example from before, this study is proposed risk management techniques that standardized rightly in the actual condition of organization with one plan, with discovery of fire risk, the feedback process in compliance with a fire risk reduction and the review which control the result is joint responsibility of engineer, technical expert and manager as part of safety management to practice with the fact must be supervised.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.1-5
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• 2018

It is proved that 'maximum' is actually attained in the following risk measure representation $${\rho}_m(X)={max \atop Q{\in}Q_m}E_Q[-X]$$.

• Health Policy and Management
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• v.25 no.3
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• pp.197-206
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• 2015

Background: The purpose of this study was to propose a method for developing a measure of hospital-wide all-cause risk-standardized readmissions using administrative claims data in Korea and to discuss further considerations in the refinement and implementation of the readmission measure. Methods: By adapting the methodology of the United States Center for Medicare & Medicaid Services for creating a 30-day readmission measure, we developed a 6-step approach for generating a comparable measure using Korean datasets. Using the 2010 Korean National Health Insurance (NHI) claims data as the development dataset, hierarchical regression models were fitted to calculate a hospital-wide all-cause risk-standardized readmission measure. Six regression models were fitted to calculate the readmission rates of six clinical condition groups, respectively and a single, weighted, overall readmission rate was calculated from the readmission rates of these subgroups. Lastly, the case mix differences among hospitals were risk-adjusted using patient-level comorbidity variables. The model was validated using the 2009 NHI claims data as the validation dataset. Results: The unadjusted, hospital-wide all-cause readmission rate was 13.37%, and the adjusted risk-standardized rate was 10.90%, varying by hospital type. The highest risk-standardized readmission rate was in hospitals (11.43%), followed by general hospitals (9.40%) and tertiary hospitals (7.04%). Conclusion: The newly developed, hospital-wide all-cause readmission measure can be used in quality and performance evaluations of hospitals in Korea. Needed are further methodological refinements of the readmission measures and also strategies to implement the measure as a hospital performance indicator.

• Industrial Engineering and Management Systems
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• v.11 no.2
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• pp.176-182
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• 2012

This paper presents a new approach to risk comparison in uncertain environment. Based on the uncertainty theory, some uncertain risk measures and risk comparison rules are proposed. Afterward the bridges are built between uncertain risk measures and risk comparison rules. Finally, several comparable examples are given.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.413-428
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• 2012

Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.287-298
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• 2013

A standard deviation has been a starting point for a mathematical definition of risk. As a remedy for drawbacks such as subadditivity property discouraging the diversification, coherent and convex risk measures are introduced in an axiomatic approach. Choquet expectation and g-expectations, which generalize mathematical expectations, are widely used in hedging and pricing contingent claims in incomplete markets. The each risk measure or expectation give rise to its own pricing rules. In this paper we investigate relationships among dynamic risk measures, Choquet expectation and dynamic g-expectations in the framework of the continuous-time asset pricing.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.377-383
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• 2016

The set of priors in the representation of coherent risk measure is expressed in terms of quantile function and increasing concave function. We show that the set of prior, $\mathcal{Q}_c$ in (1.2) is equal to the set of $\mathcal{Q}_m$ in (1.6), as maximal representing set $\mathcal{Q}_{max}$ defined in (1.7).