The article considers the problem of constructing efficient portfolio model of Tobin. Analyzed two types of portfolios: the minimum-risk and maximum profitability on the basis of quotations of oil companies of the Russian Federation (website investing.ru). A comparative analysis of stock returns of the companies and their risks with the help of software tools of MS Excel. In the course of calculations are shares of oil companies and the share of government securities built a pie chart of their percentages. Conclusions, which subsequently should affect the decision of investors.

Keywords: expected return, risk, minimum risk, maximum efficiency, securities, model of John Tobin, investment portfolio, profitability, mathematical expectation, risk free asset quotes

The article deals with the problem of formation and management of securities portfolio, which is actual for the developing economy. To solve it, an active strategy is used, which implies changes in the structure of the portfolio. The shares of assets are included in the portfolio using the Quasi – Sharpe method. The model is used in volatile stock markets for efficient performance. Research is conducted on the example of the dividends of large foreign companies Model "Quasi − Sharpe" combines the yield on a bond with a yield of a single portfolio, and the risk of the security using linear regression functions. The risk in this method is measured using the beta β coefficient, which is characterized by a degree of sensitivity to changes in the profitability of a single portfolio. Using the data Analysis package, you can find regression equations that allow you to forecast for future periods of time.

Keywords: an effective portfolio, portfolio theory, expected return, rate of return, given the risk, investment, securities, trend line, forecasting, model Quasi -Sharpe

The article discusses the problem of building a portfolio of securities. Analyzed the two models on the basis of sample data on the course of profitability of the five firms according to the site Investing.ru. A comparative analysis of risk of return of the portfolios obtained by the models of black and Markowitz. With the help of MS Excel software tools, a portfolio of minimum risk securities by Markovits is formed. Black and Markowitz models are compared, the conclusion that the investor must finally accept is formulated.

Keywords: Investments, portfolio theory, expected return, yield, variance, risk, securities, minimum risk, value, equity, black, Markowitz

The main target of sales policy in a competitive environment is customer funnel and customer loyalty. Sales approach involves encouragement of customers, vendors and business partners. Advertising is a means of a sales activity. While determining the most efficient way of distributing expenses for the purpose of advertising, it makes economic sense to use mathematical methods of programming and statistic analysis of target audience. It is able during the analysis to determine the most efficient time and location for ad placement, possible target audience and its income level. A method of calculating should be selected in order to gain more profit and incur less expenses. This is Fore and Malgrange method which allows to do so. Benefit of this method is optimality test in the process of decision making. Keywords: merchandising, advertising, sales, profit-making organization, sales approach, radio advertising, profit maximization.

Keywords: sales promotion, advertising, sales, social - demographic preferences, effective planning, profit maximization, the method Fore-Malgrange

The article presents the results of the analysis of the fluctuations of the USD/RUB and the definitions of integrability of the corresponding time series. The research of currency pair by linear methods revealed the presence of non-stationarity in the behavior of the time series, as a result we came to the conclusion that it is impossible to create a high-quality predictive model based on parametric methods.An attempt was made to improve the quality of the forecast to study the integrability of the time series. For this purpose we used various modifications of test the Dickey–Fuller and software products. We tested estimate the order of integrability of two economic time series ,characterizing fluctuations of the U.S. dollar against the ruble and the dynamics of the stock of the Sberbank. The results of the analysis prove that the Dickey-Fuller test is a simple and reliable way to assess the order of integrability of the time series. The benefits of the ADF-test before DF-test are identified.The result is a stationary model of time series , which we can used for forecasting.

Keywords: time series, the main hypothesis, alternative hypothesis, Student criterion, stationarity, nonstationarity, integrability,the test for unit root, the Dickey-Fuller test

In article the task of creation of effective portfolios of securities arising in practical investment activities is considered. Theoretical calculations decisions, necessary for creation of algorithm, are analyzed. It is noted that a basis of calculations is calculation of risk and the expected profitability of both separate assets, and all portfolio in general. For creation of model eight issuers of securities and their real course profitability in ten months according to the Moscow exchange are used. The kovariatsion matrix and a vector of the average income by means of which two effective portfolios are calculated is constructed and the assessment of their profitability and risk is carried out. According to the obtained data the effective border is simulated and displayed graphically. All necessary operations are performed by means of MS Excel.

Keywords: efficient portfolio , portfolio theory , realized a lot of expected revenue , profitability , dispersion, risk , investment , securities , envelope curve , effective border

"Dynamic mode of heat exchangers is typical for a number of technological thermal plants , as well as air-heating systems , ventilation, and air conditioning. Technologically predetermined control algorithm operating mode heat exchangers in practice implemented by means of manual or automatic adjustment in one or more control parameters . Obviously, the most efficient in the energy and technically and economically dynamic mode control algorithm of the heat exchanger can be detected only in the form of a review of the relevant mathematical model. In this paper we consider a mathematical model of the dynamic operation of the system of heat exchangers with natural air circulation . As input parameters are considered the temperature of hot and cold air streams. Modeled by changing the inputs are heat exchangers and the extent to which these changes will not affect the operation of the entire system. In order to keep the temperature at the i- MOT has not changed , the coefficient of variation should tend to zero , since all the other quantities are limited by technical parameters of the system . By changing the values ​​of the input parameters is analyzed mass flow of hot flow limits are changing the output parameters of the preceding heat exchangers that will not change the entire system ."

Keywords: heat loss into the environment, the starting temperature of the hot (cold) flow, the final temperature of the hot (cold) flow, the range of variation of hot, cold flow