# Optimal Dividend Payout under Stochastic Discounting

*Elena Bandini*,
*Tiziano de Angelis*,
*Giorgio Ferrari* and
*Fausto Gozzi*

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Elena Bandini: Center for Mathematical Economics, Bielefeld University

Tiziano de Angelis: Center for Mathematical Economics, Bielefeld University

Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University

No 636, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

**Abstract:**
Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash-flows are discounted at a stochastic dynamic rate. Dividends can be paid to shareholders at unrestricted rates so that the problem is cast as one of singular stochastic control. The stochastic interest rate is modelled by a Cox-Ingersoll- Ross (CIR) process and the firm's objective is to maximize the total expected flow of discounted dividends until a possible insolvency time. We find an optimal dividend payout policy which is such that the surplus process is kept below an endogenously determined stochastic threshold expressed as a decreasing function $r \mapsto b(r)$ of the current interest rate value. We also prove that the value function of the singular control problem solves a variational inequality associated to a second-order, non-degenerate elliptic operator, with a gradient constraint.

**Keywords:** Optimal dividend; stochastic interest rates; CIR model; singular control; optimal stopping; free boundary problems (search for similar items in EconPapers)

**Pages:** 35

**Date:** 2020-05-29

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https://pub.uni-bielefeld.de/download/2943684/2943685 First Version, 2020 (application/pdf)

**Related works:**

Journal Article: Optimal dividend payout under stochastic discounting (2022)

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**Persistent link:** https://EconPapers.repec.org/RePEc:bie:wpaper:636

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