Sincov’s and other functional equations and negative interest rates

Abstract

AbstractInvestigating the future value F(K, s, t) of a capital K invested between dates s and t, the “natural” condition $$F(K,s,t)\ge K$$ F ( K , s , t ) ≥ K has lost its naturality because of the strange fact of negative interest rates. This leads to the task of describing the possible solutions of the multiplicative Sincov equation $$f(s,u)=f(s,t)f(t,u)$$ f ( s , u ) = f ( s , t ) f ( t , u ) for $$s\le t\le u$$ s ≤ t ≤ u where $$f(s,t)=0$$ f ( s , t ) = 0 may happen. In this paper we solve this task and discuss connections to the theory of investments.