• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.29-36
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• 1998

We show that if M is a $II_1$-factor and a countable discrete group G acts outerly on M then Jones' index $[M:M^G]$ of a pair of $II_1^-factors is equal to the order $\mid$G$\mid$ of G. It is also shown that for a subgroup H of G Jones' index $[M^H:M^G]$ is equal to the group index [G:H] under certain conditions.

• Proceedings of the Optical Society of Korea Conference
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• 2005.02a
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• pp.316-317
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• 2005

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.99-110
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• 1999

We apply sector theory to obtain some characterization on Gaois groups for subfactors. As an example of a non-irreducible inclusion of small index, a locally trivial inclusion arising from an automorphism is considered and its Galois group is completely determined by using sector theory.

• Korean Management Science Review
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• v.30 no.1
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• pp.73-89
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• 2013

This paper develops an investment algorithm based on Markowitz's Portfolio Selection Theory, using historical stock return data, and empirically evaluates the performance of the proposed algorithm in the U.S. and the Hong Kong stock markets. The proposed investment algorithm is empirically tested with the 30 constituents of Dow Jones Industrial Average in the U.S. stock market, and the 30 constituents of Hang Seng Index in the Hong Kong stock market. During the 6-year investment period, starting on the first trading day of 2006 and ending on the last trading day of 2011, growth rates of 12.63% and 23.25% were observed for Dow Jones Industrial Average and Hang Seng Index, respectively, while the proposed investment algorithm achieved substantially higher cumulative returns of 35.7% in the U.S. stock market, and 150.62% in the Hong Kong stock market. When compared in terms of Sharpe ratio, Dow Jones Industrial Average and Hang Seng Index achieved 0.075 and 0.155 each, while the proposed investment algorithm showed superior performance, achieving 0.363 and 1.074 in the U.S. and Hong Kong stock markets, respectively. Further, performance in the U.S. stock market is shown to be less sensitive to an investor's risk preference, while aggressive performance goals are shown to achieve relatively higher performance in the Hong Kong stock market. In conclusion, this paper empirically demonstrates that an investment based on a mathematical model using objective historical stock return data for constructing optimal portfolios achieves outstanding performance, in terms of both cumulative returns and Sharpe ratios.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.119-125
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• 1997

We show that there exists an isomorphism between the basic construction $(M_f)_1$ for $N_f{\subset}M_f$ and the reduction $(M_1)_f$ of the basic construction $M_1$ for $N{\subset}M$, where $f$ is a nontrivial projection in N. For a nontrivial projection $f{\in}N^{\prime}{\cap}M$ we give the basic construction $(M_f)_1$ for $N_f{\subset}M_f$ and compare it with $(M_1)_f$.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.183-193
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• 1995

Let N be a $II_1$ factor and G be a finite group acting outerly on N. Then the crossed product algebra $M = N \rtimes G$ is also a $II_1$ factor and $N' \cap M = CI$, i.e. N is irreducible in M. Moreover, N is regular in M, in other words, M is generated by the normalizer $N_M (N)$.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.1
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• pp.36.4-37
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• 2017

Although most of observed properties of giant radio relics detected in the outskirts of galaxy clusters could be explained by relativistic electrons accelerated at merger-driven shocks, a few significant puzzles remain. In some relics the shock Mach number inferred from X-ray observations is smaller than that estimated from radio spectral index. Such a discrepancy could be understood, if either the shock Mach number is nder-estimated in X-ray observation due to projection effects, or if pre-existing electrons with a flat spectrum are re-accelerated by a weak shock, retaining the flat spectral form. In this study, we explore these two scenarios by comparing the results of shock acceleration simulations with observed features of the so-called Toothbrush relic in the merging cluster 1RXS J060303.3. We find that both models could reproduce reasonably well the observed radio flux and spectral index profiles and the integrated radio spectrum. Either way, the broad transverse relic profile requires additional post shock electron acceleration by downstream turbulence.

• Journal of Korea Port Economic Association
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• v.27 no.1
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• pp.263-280
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• 2011

The global financial crisis, triggered by the subprime mortgage crisis in 2007, has put the world economy into the recession with financial market turmoil. I tested whether variables were cointegrated or whether there was an equilibrium relationship. Also, Generalized impulse-response function (GIRF) and accumulation impulse-response function (AIRF) may be used to understand and characterize the time series dynamics inherent in economical systems comprised of variables that may be highly interdependent. Moreover, the IRFs enables us to simulate the response in freight to a shock in the USD/JPY exchange rate, Dow Jones industrial average index, Dow Jones volatility, Chinese Import volatility. The result on the cointegration test show that the hypothesis of no cointergrating vector could be rejected at the 5 percent level. Also, the empirical analysis of cointegrating vector reveals that the increases of USD/JPY exchange rate have negative relations with freight. The result on the impulse-response analysis indicate that freight respond negatively to volatility, and then decay very quickly. Consequently, the results highlight the potential usefulness of the multivariate time series techniques accounting to behavior of Freight.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.7
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• pp.27-34
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• 2020

The study investigates herding behavior in cryptocurrencies in different situations. This study employs daily returns of major cryptocurrencies listed in CCI30 index and sub-major cryptocurrencies and major stock returns listed in Dow-Jones Industrial Average Index, from 2015 to 2018. Quantile regression method is employed to test the herding effect in market asymmetries, inter-dependency and intra-dependency cases. Findings confirm the presence of herding in cryptocurrency in upper quantiles in bullish and high volatility periods because of overexcitement among investors, which lead to high volume trading. Major cryptocurrencies cause herding in sub-major cryptocurrencies, but it is a unidirectional relation. However, no intra-dependency effect among cryptocurrencies and equity market is observed. Results indicate that in the CKK model herding exists at upper quantile in market that may be due when the market is moving fast, continuously trading, and bullish trend are prevailing. Further analysis confirms this narrative as, at upper quantile, the beta of bullish regime is negative and significant, meaning the main source of market herding is a bullish trend in investment, which increases market turbulence and gives investors opportunity to herd. Also, we found that herding in cryptocurrencies exits in high volatility periods, but this herding mostly depends on market activity, not market movement.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.2
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• pp.725-735
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• 2021

This study investigates whether the Islamic Exchange-Traded Funds (ETFs) provide significant benefit to investors relative to conventional ETFs. Six pairs of Islamic and conventional ETFs with 10-year daily price data from 2010 to 2019 have been selected from major market indices like MSCI World Index, MSCI Emerging Markets, MyETF Dow Jones Islamic Market Malaysia, MSCI South East Asia and Wahed FTSE Shariah USA Index for this study. For ETFs that are launched after 2010, the price data from launch date to 2019 are used. Our results show: First, Islamic ETFs are more likely to trade at a premium rather than at a discount, implying the investors are willing to pay a premium. Second, it is also found that Islamic ETFs have a relatively shorter period of price deviation from the benchmark, implying more price stability. Third, conventional ETFs have higher return and lower tracking errors relative to Islamic ETFs. These new findings add to the stylized facts of Islamic ETFs in the extant literature for investors, plan sponsors and regulators as to the differences between the ETFs. As policy suggestion, asset management companies can design new investment products to bridge the gap between conventional and Islamic finance.