Results found: 2

Search results

Sort By:

Limit search:

EXPONENTIAL DERIVATIVE AND RATE OF INTEREST

100%

Janaszak T.

Przegląd Statystyczny

2005

vol. 52

issue 4

41-59

Rate of interest is said a parameter of growth of the capital. In the paper a way is presented from the idea of a parameter to the idea of geometrical and algebraic object. If the economic process is said a real function, then the rate of interest is a local property of the function. In classical theory a local rate of interest is defined with application of classic calculus. The classic calculus is constructed with application of linear function. Classic derivative is the straight tangent line of the process. In financial mathematics is made the research of relationship between relative expansion of the value of the function and absolute expansion of the argument of the function. The adequate instrument of the research is not the straight tangent line but the exponential tangent line. With collection of exponential lines the construction of basic concepts of classic calculus is possible. The rate of interest is the exponential derivative in a point of the function. In financial mathematics this is adequate method of research.

THE TANGENT LINES AND LOCAL PROPERTY

100%

Janaszak T.

Przegląd Statystyczny

2005

vol. 52

issue 2

23-39

In this paper the local property of economic processes is considered. The economic-process is said a real function and its shape is global property of economic process. The local property of !he processes is an algebraic expression. Each expression contains: the derivative of the function, and alternatively the value of the function, or the value of the argument of the function; it is represented by an tangent line to the process. For example: marginal value of the process is a coefficient of proportionality for expansion of the function; 'dy' and expansion of the argument: 'dx', so it is the classic linear derivative of the process: 'y' . The marginal value is represented by linear function tangent to the process. Logarithmic derivative of the process as well as its elasticity are also presented in the mathematical form. The paper presents an universal construction of tangent lines. First, the construction is made in the language of the theory of sets. The local property is said a function tangent to the process. Later the universal model is filled up with the theory of group. For the construction of tangent function two elements are needed: a principle of tangent and advisable class of functions. The class is correlated with the principle. Each function of the advisable class is not tangent to the other function of the class. Principle of tangent is a relation of equivalent. The advisable class of the function is said a class of derivatives. Derivative of any function is a function of the advisable class. Any function has got one derivative or no derivative. In the construction of derivative in language of the theory of group the mapping from a topological group into any group is considered. The principle of tangent is defined by the local topology of the Cartesian product of the groups. These constructions include classic calculus and parallel calculus with mappings:linear, exponential, power and logarithmic

Refine search results

2 Przegląd Statystyczny

2 Janaszak T.

2 2005

Search results

EXPONENTIAL DERIVATIVE AND RATE OF INTEREST

THE TANGENT LINES AND LOCAL PROPERTY