By a payment stream one understands a function, which indicates for time intervals, how much money flowed into which direction. It is thus related to density functions.

Definition

A payment stream can general be defined in such a way:

• Is
  • Current values \ mathbb {} the quantity of all times, which we regard,
  • Monetary values \ mathbb {} the quantity of all monetary values (e.g. the quantity of all possible account balances), which we regard,
  • z: Current values \ rightarrow monetary values a function.
• Exactly then applies:
  • z \ mathbb {} is called payment stream.

Usually negative monetary values for disbursements, positive monetary values for deposits are used.

discrete payment stream

Above definition does not state yet much over the kind of the quantity of current values \ mathbb {}. This can be e.g. constant or discrete. In academic examples she is often selected as discrete, since constant payment stream often cannot be presented so well. If the definition quantity of a payment stream z is discrete \ mathbb {}, then this payment stream is called likewise discrete.

Such a discrete payment stream is then often represented as discrete payment vector. This lists simply the values of the payment stream on neighbouring discrete times.

Linear combination

Payment stream of same type can be added, by being added point for point. Payment stream of same type leave themselves multiplied by a constant out \ mathbb {to R}, by being multiplied point for point by it.

Vector space

Payment stream of same type stretch in each case a vector space.

further definition, economic meaning

Payment stream one - primarily - calls evenly running, constantly returning, payments. As it e.g. in an annuity loan or in an installment credit occur. In these cases one speaks of an even payment stream.

With credits and loans - which are not suspended for repayment - the payment stream sits down to a repayment portion together in each case from a share of interest and and. While with an installment credit interest and repayment portion remain unchanged over the entire running time of the credit, interest and repayment portion change with an annuity loan with each rate. The share of interest falls thereby continuously, in response rises the repayment portion continuously.

On the basis the payment stream - in the case of doubt - a complete back calculation can be made by credits and loans by credit-oh-reasonable. This is in controversies of substantial importance. There are cases, in which differences of some thousands EURO furnished the recalculation of payment stream.

In this connection increasingly also the unkorrekte validity is criticized by by the credit institutes, which lead in the case of doubt to a increased interest load.

See also

• Spanning condition
• Cash-flow: Special payment stream of an enterprise

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