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State-space approach to capital return in nonlinear growth processes

Petri P. Kärenlampi (Faculty of Science and Forestry, University of Eastern Finland, Joensuu, Finland)

Agricultural Finance Review

ISSN: 0002-1466

Article publication date: 21 August 2019

Issue publication date: 2 September 2019




The purpose of this paper is to introduce a capital return rate function for growth processes, and apply it to financial sustainability considerations in growing multiannual plants.


A partition function of change rate of capitalization is introduced, as well as that of capitalization itself, and the expected value of capital return rate is produced as the ratio of the two functions.


Financial sustainability significantly differs from maximum-yield sustainability, and does not depend on any external interest rate.

Research limitations/implications

It is proposed that financial considerations should not be based on any arbitrary external interest. Neither should the shape of any yield function be neglected. Constancy of capital return rate in time is not assumed.

Practical implications

Two forestry examples show that the capital return rate is sensitive to rotation time, and in particular to the level of initial investment. The proposed procedure can be applied in the absence of periodic boundary conditions in time.


The methodology has not been applied in this field previously.



The authors do not have any particular interest to declare in relation to this paper.


Kärenlampi, P.P. (2019), "State-space approach to capital return in nonlinear growth processes", Agricultural Finance Review, Vol. 79 No. 4, pp. 508-518.



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