• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.311-335
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• 2022

This paper treats Merton's classical portfolio optimization problem for a market participant who invests in safe assets and risky assets to maximize the expected utility. When the state process is a d-dimensional Markov diffusion, this problem is transformed into a problem of solving a Hamilton-Jacobi-Bellman (HJB) equation. The main purpose of this paper is to solve this HJB equation by a deep learning algorithm: the deep Galerkin method, first suggested by J. Sirignano and K. Spiliopoulos. We then apply the algorithm to get the solution to the HJB equation and compare with the result from the finite difference method.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.1031-1046
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• 2001

The paper studies the evolution of the financial markets and pays the basic attention to the role of financial innovations (derivative securities) in this process. A characterization of both complete and incomplete markets is given through an identification of the sets of contingent claims and terminal wealths of self-financing portfolios. the dynamics of the financial system is described as a movement of incomplete markets to a complete one when the volume of financial innovations is growing up and the spread tends to zero (the Merton financial innovation spiral). Namely in this context the paper deals with the problem of pricing risks in both field: finance and insurance.

• Journal of Intelligence and Information Systems
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• v.26 no.2
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• pp.105-129
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• 2020

This study uses corporate data from 2012 to 2018 when K-IFRS was applied in earnest to predict default risks. The data used in the analysis totaled 10,545 rows, consisting of 160 columns including 38 in the statement of financial position, 26 in the statement of comprehensive income, 11 in the statement of cash flows, and 76 in the index of financial ratios. Unlike most previous prior studies used the default event as the basis for learning about default risk, this study calculated default risk using the market capitalization and stock price volatility of each company based on the Merton model. Through this, it was able to solve the problem of data imbalance due to the scarcity of default events, which had been pointed out as the limitation of the existing methodology, and the problem of reflecting the difference in default risk that exists within ordinary companies. Because learning was conducted only by using corporate information available to unlisted companies, default risks of unlisted companies without stock price information can be appropriately derived. Through this, it can provide stable default risk assessment services to unlisted companies that are difficult to determine proper default risk with traditional credit rating models such as small and medium-sized companies and startups. Although there has been an active study of predicting corporate default risks using machine learning recently, model bias issues exist because most studies are making predictions based on a single model. Stable and reliable valuation methodology is required for the calculation of default risk, given that the entity's default risk information is very widely utilized in the market and the sensitivity to the difference in default risk is high. Also, Strict standards are also required for methods of calculation. The credit rating method stipulated by the Financial Services Commission in the Financial Investment Regulations calls for the preparation of evaluation methods, including verification of the adequacy of evaluation methods, in consideration of past statistical data and experiences on credit ratings and changes in future market conditions. This study allowed the reduction of individual models' bias by utilizing stacking ensemble techniques that synthesize various machine learning models. This allows us to capture complex nonlinear relationships between default risk and various corporate information and maximize the advantages of machine learning-based default risk prediction models that take less time to calculate. To calculate forecasts by sub model to be used as input data for the Stacking Ensemble model, training data were divided into seven pieces, and sub-models were trained in a divided set to produce forecasts. To compare the predictive power of the Stacking Ensemble model, Random Forest, MLP, and CNN models were trained with full training data, then the predictive power of each model was verified on the test set. The analysis showed that the Stacking Ensemble model exceeded the predictive power of the Random Forest model, which had the best performance on a single model. Next, to check for statistically significant differences between the Stacking Ensemble model and the forecasts for each individual model, the Pair between the Stacking Ensemble model and each individual model was constructed. Because the results of the Shapiro-wilk normality test also showed that all Pair did not follow normality, Using the nonparametric method wilcoxon rank sum test, we checked whether the two model forecasts that make up the Pair showed statistically significant differences. The analysis showed that the forecasts of the Staging Ensemble model showed statistically significant differences from those of the MLP model and CNN model. In addition, this study can provide a methodology that allows existing credit rating agencies to apply machine learning-based bankruptcy risk prediction methodologies, given that traditional credit rating models can also be reflected as sub-models to calculate the final default probability. Also, the Stacking Ensemble techniques proposed in this study can help design to meet the requirements of the Financial Investment Business Regulations through the combination of various sub-models. We hope that this research will be used as a resource to increase practical use by overcoming and improving the limitations of existing machine learning-based models.

• Korean Security Journal
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• no.1
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• pp.371-408
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• 1997

This article is the reserch on actual condition of crime of arson which occurs in Korea and its countermeasures. The the presented problem in this article are that (1) we have generally very low rate concern about the crime of arson contrary to realistic problems of rapid increase of crime of arson (2) as such criminal motives became so diverse as to the economic or criminal purpose unlike characteristic and mental deficiency of old days, and to countermeasure these problems effectively it presentation the necessity of systemantic research. Based on analysis of reality of arson, the tendency of this arson in Korea in the ratio of increase is said to be higher than those in violence crime or general fire rate. and further its rate is far more greater than those of the U.S.A. and Japan. Arson is considered to be a method of using fire as crime and in case of presently residence to be the abject, it is a public offense crime which aqccompany fatality in human life. This is the well It now fact to all of us. And further in order to presentation to the crime of arson, strictness of criminal law (criminal law No, 164 and 169, and fire protection law No. 110 and 111) and classification of arsonist as felony are institutionary reinforced to punish with certainty of possibility, Therefore, as tendency of arson has been increased compared to other nations, it is necessary to supplement strategical policy to bring out overall concerns of the seriousness of risk and damage of arson, which have been resulted from the lack of understanding. In characteristics analysis of crime of arson, (1) It is now reveald that, in the past such crime rate appeared far more within the boundary of town or city areas in the past, presently increased rate of arsons in rural areas are far more than in the town or small city areas, thereby showing characteristics of crime of arson extending nation wide. (2) general timetable of arson shows that night more than day time rate, and reveald that is trait behavior in secrecy.(3) arsonists are usually arrested at site or by victim or report of third person(82,9%).Investigation activities or self surrenders rate only 11.2%. The time span of arrest is normally the same day of arson and at times it takes more than one year to arrest. This reveals its necessity to prepare for long period of time for arrest, (4) age rate of arson is in their thirties mostly as compared to homicide, robbery and adultery, and considerable numbers of arsons are in old age of over fifties. It reveals age rate is increased (5) Over half of the arsonists are below the junior high school (6) the rate of convicts by thier records is based on first offenders primarily and secondly more than 4 time convicts. This apparently shows necessity of effective correctional education policy for their social assimilation together with re-investigation of human education at the primary and secondary education system in thier life. The examples of motivation for arosnits, such as personal animosity, fury, monetary swindle, luscious purpose and other aims of destroying of proof, and other social resistance, violence including ways of threatening, beside the motives of individual defects, are diverse and arsonic suicide and specifically suicidal accompany together keenly manifested. When we take this fact with the criminal theory, it really reveals arsons of crime are increasing and its casualities are serious and a point as a way of suicide is the anomie theory of Durkheim and comensurate with the theory of that of Merton, Specifically in the arson of industrial complex, it is revealed that one with revolutionary motive or revolting motive would do the arsonic act. For the policy of prevention of arsons, professional research work in organizational cooperation for preventive activities is conducted in municipal or city wise functions in the name of Parson Taskforces and beside a variety of research institutes in federal government have been operating effectively to countermeasure in many fields of research. Franch and Sweden beside the U.S. set up a overall operation of fire prevention research funtions and have obtained very successful result. Japan also put their research likewise for countermeasure. In this research as a way of preventive fire policy, first, it is necessary to accomodate the legal preventitive activities for fire prevention in judicial side and as an administrative side, (1) precise statistic management of crime of arson (2) establishment of professional research functions or a corporate (3) improvement of system for cooperative structural team for investigation of fires and menpower organization of professional members. Secondly, social mentality in individual prospect, recognition of fires by arson and youth education of such effect, educational program for development and practical promotion. Thirdly, in view of environmental side, the ways of actual performance by programming with the establishment of cooperative advancement in local social function elements with administrative office, habitants, school facilities and newspapers measures (2) establishment of personal protection where weak menpowers are displayed in special fire prevention measures. These measures are presented for prevention of crime of arson. The control of crime and prevention shall be prepared as a means of self defence by the principle of self responsibility Specifically arsonists usually aims at the comparatively weak control of fire prevention is prevalent and it is therefore necessary to prepare individual facilities with their spontaneous management of fire prevention instead of public municipal funtures of local geverment. As Clifford L. Karchmer asserted instead of concerns about who would commit arson, what portion of area would be the target of the arson. It is effective to minister spontaveously the fire prevention measure in his facility with the consideration of characteristics of arson. On the other hand, it is necessary for the concerned personnel of local goverment and groups to distribute to the local society in timely manner for new information about the fire prevention, thus contribute to effective result of fire prevention result. In consideration of these factors, it is inevitable to never let coincide with the phemonemon of arsons in similar or mimic features as recognized that these could prevail just an epedemic as a strong imitational attitude. In processing of policy to encounter these problems, it is necessary to place priority of city policy to enhancement of overall concerns toward the definitive essense of crime of arson.