Non-Linear Stochastic Fractional programming models provide numerous insights into a wide variety of
areas such as financial derivatives. Portfolio optimization has been one of the important research fields
in modern finance. The most important character within this optimization problem is the uncertainty of
the future returns on assets. The objective of this study is to achieve maximum profit with minimum
investment in the stock market. In this paper, we have discussed about linear and non-linear stochastic
fractional programming problems with mixed constraints, which is the key aspect of this model. The
application of the model is discussed with an example.
Let us define what are financial derivatives. A derivative is a financial instrument whose
value is derived from the price of a more basic asset called the underlying. The underlying
may not necessarily be a tradeable product. Examples of underlyings are stock market
indices, shares, commodities, currencies, credits, weather forecasts, sunshine, results of
sport matches, wind speed and so on. Basically, anything that may have a certain degree
of an unpredictable effect on any business activity can be considered as an underlying of
a certain derivative. The most popular derivative is the stock option.
Before we discuss about stock options, we should know what an investment is. An
investment is a sacrifice of current money for future benefits (Prasanna [8]). Nowadays
a number of avenues of investment are available. One can have chances of investing the
money in the form of, depositing money in a bank account or purchase a long-term
government bond or invest in the equity shares of a company or contribute to provident
fund account or buy a stock option or acquire a plot of land.
Important attributes of any investment are time and risk. The sacrifice takes place now
and is certain. The benefit is expected in the future and tends to be uncertain and here
the stochastic nature is peeping into the picture. One can find stochastic models in Robert
A Strong [9] and Sen [10]. In some investments, the time element is the vital attribute
and in some other investments the risk factor is the vital attribute. For example, in
government bonds, time plays a vital role whereas in stock options, risk matters. |
