1. Description of the subject area (4 tasks)

    Sources of income (SI) are here securities of any types (stocks, bonds, etc.), acquired on the stock exchange and subsequently sold in the same place with the aim of deriving a financial benefit. The latter is formed by difference between prices of the future sale and the purchase of the same securities and by receiving dividends from their temporary ownership.

     We consider four solvable tasks on finding optimal strategies of investing funds in acquisition of such SI from a given set of them, when is maximized the absolute income from realization of acquired earlier SI and their previous exploitation.

     There are two options of SI realization:

  • through a certain period of time (task 1);
  • on their definite profitability, when you have the following three options of payback factor:
    • without return (task 2);
    • return on investment in absence of initial SI (task 3);
    • return on initial SI cost in absence of investment (task 4).

     For all these four tasks takes place a random varying profitability (see definit. below). At that, the value of a SI sample of some type is a known fixed value, and its parameters of profitability or future realization are random variables. This implies, that there is a risk if investment, and a risk of exceeding the permissible period of its return (if there is such a term). The values ​​of these risks are estimated by statistical modeling of an optimized process of investing in a given set of SI.

Definition. Varying profitability is called a property of SI to change their profitability either forced (under some control), or under the influence of some random factors. In our case SI are securities, which selling prices are determined by market price trends, therefore here takes place a random varying profitability.

Note 1. Risk of investment is characterized by the following parameters: a given probability of the risk ofobtaining not more value of absolute income from realization of acquired SI than the value of threshold income, which is determined by modeling of the found optimal investment strategy.

Note 2. Return on investment (in absence of initial SI) or return on initial SI cost (in absence of investment) takes place in case when actual proceeds from realization for a specified period of acquired SI will not be less thana returm sum, which is equal to the product of a cost of this SI by a given rate of return.

     The main difference of the task 1 from the group of tasks 2–4 is that for it is considered a nonstandard case of SI realization, when all earlier purchased SI are sold through a fixed period of time, that has elapsed since their purchase, without taking into account their current profitability.

     Standard case of SI realization, which is typical for exchange trade of securities, is considered in tasks 2–4. It consists in the fact that the SI of each type are sold according to their market value. In other words, the being found optimal strategy of investment indicates how many SI of each type should be bought at initial prices and at what more higher prices all of them should then be sold.

     To solve the last three tasks you need to know for each SI type the tabular functions of distribution of random time intervals until appearance on the exchange of requests for purchase on specified different prices of this SI sample, which exceed its known initial price (it is defined in the task as a cost of one SI of this type). Such distribution functions, which represent probability characteristics of future prices for SI of different types, should be formed in a specialized program, which performs an operation of forecasting market prices of SI. The presence of these characteristics for different-type securities sold on the stock exchange, is a prerequisite for a successful solution of tasks 2–4.

     All these four tasks on optimizing investments in securities are a particular case of the tasks of seven types on optimizing investments in any SI. They can be solved numerically by using the new science-intensive network technology called "Information technology of automation of control of discrete technological and information processes (in short — IT AC DTIP)", because optimizable process has all necessary properties for that. This process is discrete and is classified as an instant process of selecting choices. Its elements in terms of DTIP are:

  • securities — demands;
  • amount of investment — a device of service.