Submit a 2500 words essay on the topic Portfolio Optimization using Linear, Non-linear and Integer programming and Black-schole theroy.Portfolio optimization dwells on the improvement of the portfolio and improving the value and level of the stock portfolio to that which proves attractive to the market. The criterion allows for the combination of the various aspects either directly or indirectly. The optimization aspect allows for the analysis of the expected value and the rate of return and their dispersion. The dispersion looks at the distribution of the rate of return to the stock adding value to it and through these measures, the financial risks also undergo analysis to provide evidence and confidence in the investors. Its through portfolio optimization that investors understand the various risks existing in the market that allows them.Portfolio optimization will require identification of a portfolio that is rich in diversification to ensure it provides good support to the portfolio. Following the yahoo finance, the following portfolio was considered. Considering the modern portfolio theory as developed by Harry Markowitz, standard deviation of the various portfolios and its rate of return as means of maximizing the expected returns are considered for the risks that may engulf the portfolio. These provide an efficient portfolio. Considering the trade-off between the risks involved with the expected returns that the portfolio covers. Considering the historical factors of the stocks provides the investors with better decisions on the direction of the stock overtime. These based on the curves on the value of the stocks, its prices and volumes traded. Considering the standard deviation, the volatility of the stock, and the stock prices and volumes provides a better position on the stock. Considering these enables, the investors provide a better response to their portfolio needs.Considering the initial portfolio selection, the following portfolio is
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