We consider mean-risk portfolio optimisation models, with risk measured by symmetric measures (variance) as well as downside or tail measures (lower partial moments, conditional value at risk). A framework for including index options in the universe of assets, in addition to stocks, is provided. The exercise of index options is settled in cash, making this implementable with a variety of strike prices and maturities. We use a dataset with stocks from FTSE 100 and index options on FTSE100. Numerical results show that, for low risk-low return and to medium risk-medium return portfolios, the addition of an index put further reduces the risk to a considerable extent, particularly in the case of mean-CVaR efficient portfolios, where the left tail of the portfolio return distribution is dramatically improved. For high risk-high return portfolios, the inclusion of an index call improves the right tail of the return distribution, creating thus the opportunity for considerably higher returns.
A good investment portfolio is a properly selected group of investment products such as stocks, bonds and cash equivalents. On top of grouping a brilliant portfolio, an excellent portfolio manager will consider the risk of downturn in financial performance as an important event that need to be taken care of at it best. This paper focuses on managing this risk of a welldiversified investment portfolio. The focus is to be narrowed down into finding the assurance value of the risk. This assurance value will be evaluated under specific strategy of buying traded European put option. The most celebrated Black-Scholes model to option pricing will be used in determining the values of these portfolio insurance strategies. General input parameters such as volatility and dividend yields of the portfolio will be taken from the performance of FTSE Bursa Malaysia KLCI (FTSEBMKL) as the portfolio is reflected by the performance on the index. The value results will be then viewed as numerical evaluation of some well-diversified portfolio examples, which will vary in term of specific input parameters of certain cases. This study provides straightforward insurance strategies a portfolio manager would have done in managing risk of downturn in the financial market. This strategy structure could be further enhanced by considering various other financial tools that are available or to be made available in the financial world.
A mammography provides a grayscale image of the breast. The main challenge of analyzing mammography images is to extract the region boundary of the breast abnormality for further analysis. In computer vision, this method is also known as image segmentation. The variational level set mathematical model has been proven to be effective for image segmentation. Several selective types of variational level set models have recently been formulated to accurately segment a specific object on images. However, these models are incapable of handling complex intensity inhomogeneity images, and the segmentation process tends to be slow. Therefore, this study formulated a new selective type of the variational level set model to segment mammography images that incorporate a machine learning algorithm known as Self-Organizing Map (SOM). In addition to that, the Gaussian function was applied in the model as a regularizer to speed up the processing time. Then, the accuracy of the segmentation’s output was evaluated using the Jaccard, Dice, Accuracy and Error metrics, while the efficiency was assessed by recording the computational time. Experimental results indicated that the new proposed model is able to segment mammography images with the highest segmentation accuracy and fastest computational speed compared to other iterative models.
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