Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate

Julia Eisenberg, Stefan Kremsner and Alexander Steinicke
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Julia Eisenberg: Department of Financial and Actuarial Mathematics, TU Wien, Wiedner Hauptstraße 8–10/E105-1, 1040 Vienna, Austria
Stefan Kremsner: Department of Mathematics, University of Graz, Heinrichstraße 36, 8010 Graz, Austria
Alexander Steinicke: Department of Mathematics and Information Technology, Montanuniversitaet Leoben, Peter Tunner-Straße 25/I, 8700 Leoben, Austria

Mathematics, 2021, vol. 9, issue 18, 1-20

Abstract: We investigate a dividend maximization problem under stochastic interest rates with Ornstein-Uhlenbeck dynamics. This setup also takes negative rates into account. First a deterministic time is considered, where an explicit separating curve ? ( t ) can be found to determine the optimal strategy at time t . In a second setting, we introduce a strategy-independent stopping time. The properties and behavior of these optimal control problems in both settings are analyzed in an analytical HJB-driven approach, and we also use backward stochastic differential equations.

Keywords: optimal control; dividends; stochastic interest rate; Hamilton–Jacobi–Bellman equation; HJB; finite time horizon; backward stochastic differential equation; BSDE (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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