Sincov’s and Other Functional Equations and Negative Interest Rates

Kiss, Gergely and Schwaiger, Jens (2023) Sincov’s and Other Functional Equations and Negative Interest Rates. AEQUATIONES MATHEMATICAE, 97 (3). pp. 629-637. ISSN 0001-9054 (print); 1420-8903 (online)

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Abstract

Investigating the future value F(K, s, t) of a capital K invested between dates s and t, the “natural” condition 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) for s≤ t≤ u where f(s, t) = 0 may happen. In this paper we solve this task and discuss connections to the theory of investments.

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