• The Korean Journal of Financial Management
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• v.26 no.1
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• pp.165-188
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• 2009

This paper has suggested the methodology for the frontier portfolios and the optimal portfolio under the mean-VaR framework, not assuming the normal distribution and considering the investor's preferences for the higher moments of return distributions. It suggested the grid and rank approach which did not need an assumption about return distributions to find the frontier portfolios. And the optimal portfolio was selected using the utility function that considered the 3rd and the 4th moments. For the application of the methodology, weekly returns of the developed countries index, the emerging market index and the KOSPI index were used. After the frontier portfolios of the mean-variance framework and the mean-VaR framework were selected, the optimal portfolios of each framework were compared. This application compared not only the difference of the standard deviation but also the difference of the utility level and the certainty equivalent expressed by weekly expected returns. In order to verify statistical significances about the differences between the mean-VaR and the mean-variance, this paper presented the statistics which were obtained by the historical simulation method using the bootstrapping. The results showed that an investor under the mean-VaR framework had a tendency to select the optimal portfolio which has bigger standard deviation, comparing to an investor under the mean-variance framework. In addition, the more risk averse an investor is, the bigger utility level and certainty equivalent he achieves under the mean-VaR framework. However, the difference between the two frameworks were not significant in statistical as well as economic criterion.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• East Asian mathematical journal
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• v.38 no.3
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• pp.277-292
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• 2022

This study investigates the convergence of the optimal consumption and investment policies in a binomial-tree model to those in the continuous-time model of Merton (1969). We provide the convergence in explicit form and show that the convergence rate is of order ∆t, which is the length of time between consecutive time points. We also show by numerical solutions with realistic parameter values that the optimal policies in the binomial-tree model do not differ significantly from those in the continuous-time model for long-term portfolio management with a horizon over 30 years if rebalancing is done every 6 months.

• Journal of Korean Society for Quality Management
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• v.51 no.4
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• pp.573-588
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• 2023

Purpose: This study presents a research approach that utilizes deep reinforcement learning to construct optimal portfolios based on the business cycle for stocks and other assets. The objective is to develop effective investment strategies that adapt to the varying returns of assets in accordance with the business cycle. Methods: In this study, a diverse set of time series data, including stocks, is collected and utilized to train a deep reinforcement learning model. The proposed approach optimizes asset allocation based on the business cycle, particularly by gathering data for different states such as prosperity, recession, depression, and recovery and constructing portfolios optimized for each phase. Results: Experimental results confirm the effectiveness of the proposed deep reinforcement learning-based approach in constructing optimal portfolios tailored to the business cycle. The utility of optimizing portfolio investment strategies for each phase of the business cycle is demonstrated. Conclusion: This paper contributes to the construction of optimal portfolios based on the business cycle using a deep reinforcement learning approach, providing investors with effective investment strategies that simultaneously seek stability and profitability. As a result, investors can adopt stable and profitable investment strategies that adapt to business cycle volatility.

• Journal of the Korean Operations Research and Management Science Society
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• v.38 no.4
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• pp.35-52
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• 2013

Markowitz's portfolio selection model is used to construct an optimal portfolio which has minimum variance, while satisfying a minimum required expected return. The model uses estimators based on analysis of historical data to estimate the returns, standard deviations, and correlation coefficients of individual stocks being considered for investment. However, due to the inaccuracies involved in estimations, the true optimality of a portfolio constructed using the model is questionable. To investigate the effect of estimation inaccuracy on actual portfolio performance, we study the changes in a portfolio's realized return and standard deviation as the accuracy of the estimations for each stock's return, standard deviation, and correlation coefficient is increased. Furthermore, we empirically analyze the portfolio's performance by comparing it with the performance of active mutual funds that are being traded in the Korean stock market and the KOSPI benchmark index, in terms of portfolio returns, standard deviations of returns, and Sharpe ratios. Our results suggest that, among the three input parameters, the accuracy of the estimated returns of individual stocks has the largest effect on performance, while the accuracy of the estimates of the standard deviation of each stock's returns and the correlation coefficient between different stocks have smaller effects. In addition, it is shown that even a small increase in the accuracy of the estimated return of individual stocks improves the portfolio's performance substantially, suggesting that Markowitz's model can be more effectively applied in real-life investments with just an incremental effort to increase estimation accuracy.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.2
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• pp.83-95
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• 2014

In this paper, we develop a portfolio selection model that can be used to invest in markets with margin requirements such as the foreign exchange market. An investment algorithm to implement the proposed portfolio selection model based on objective historical data is also presented. We further conduct empirical analysis on the performance of a hypothetical investment in the foreign exchange market, using the proposed portfolio selection model and investment algorithm. Using 7 currency pairs that recorded the highest trading volume in the foreign exchange market during the most recent 10 years, we compare the performance of 1) the Dollar Index, 2) a 1/N Portfolio which equally allocates capital to all N assets considered for investment, and 3) a hypothetical investment portfolio selected and managed according to the portfolio selection model and investment algorithm proposed in this paper. Performance is compared in terms of accumulated returns and Sharpe ratios for the 10-year period from January 2003 to December 2012. The results show that the hypothetical investment portfolio outperforms both benchmarks, with superior performance especially during the period following financial crisis. Overall, this paper suggests that a mathematical approach for selecting and managing an optimal investment portfolio based on objective data can achieve outstanding performance in the foreign exchange market.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.4
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• pp.137-152
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• 2014

In this paper, I suggest several techniques to estimate covariance matrix and compare the performance of the global minimum variance portfolio (GMVP) in terms of out of sample mean standard deviation and return. As a result, the return differences among the GMVPs are insignificant. The mean standard deviation of the GMVP using historical covariance is sensitive to the estimation window and the number of assets in the portfolio. Among the model covariance, the GMVP using constant systematic risk ratio model or using short sale restriction shows the best performance. The performance difference between the GMVPs using historical covariance and model covariance becomes insignificant as the historical covariance is estimated with longer estimation window. Lastly, the implied volatilities from ELW prices do not lead to superior performance to the historical variance.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.12
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• pp.1169-1172
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• 2006

The prices of chemical products are fluctuated by several factors. The chemical companies can't predict and be ready to all of these changes, so they are exposed to the risk of a profit fluctuation. But they can reduce this risk by making a well-diversified product portfolio. This problem can be thought as the optimization of the product portfolio. We assume that the profits come from the 'spread' between a naphtha and a chemical product. We calculate a mean and a variation of each spread and develop an automatic module to calculate the optimal portion of each product. The theory is based on the Markowitz portfolio management. It maximizes the expected return while minimizing the volatility. At last we draw an investment selection curve to compare each alternative and to demonstrate the superiority. And we suggest that an investment selection curve can be a decision-making tool.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.219-225
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• 2014

I use the dynamic programming approach to study the optimal consumption and investment problem with regime-switching and constant labor income. I derive the optimal solutions in closed-form with constant absolute risk aversion (CARA) utility and constant disutility.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.85-90
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• 2013

We use the dynamic programming method to investigate the optimal consumption and investment problem with regime-switching. We derive the optimal solutions in closed-form with constant absolute risk aversion (CARA) utility.