Optimal Dividend Payout under Stochastic Discounting

Bandini E, de Angelis T, Ferrari G, Gozzi F (2020) Center for Mathematical Economics Working Papers; 636.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Bandini, Elena; de Angelis, Tiziano; Ferrari, GiorgioUniBi; Gozzi, Fausto
Abstract / Bemerkung
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.

2010 Mathematics Subject Classification. 91G50, 93E20, 60G40, 35R35
Stichworte
Optimal dividend; stochastic interest rates; CIR model; singular control; optimal stopping; free boundary problems
Erscheinungsjahr
2020
Band
636
Seite(n)
35
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2943684

Zitieren

Bandini E, de Angelis T, Ferrari G, Gozzi F. Optimal Dividend Payout under Stochastic Discounting. Center for Mathematical Economics Working Papers. Vol 636. Bielefeld: Center for Mathematical Economics; 2020.
Bandini, E., de Angelis, T., Ferrari, G., & Gozzi, F. (2020). Optimal Dividend Payout under Stochastic Discounting (Center for Mathematical Economics Working Papers, 636). Bielefeld: Center for Mathematical Economics.
Bandini, E., de Angelis, T., Ferrari, G., and Gozzi, F. (2020). Optimal Dividend Payout under Stochastic Discounting. Center for Mathematical Economics Working Papers, 636, Bielefeld: Center for Mathematical Economics.
Bandini, E., et al., 2020. Optimal Dividend Payout under Stochastic Discounting, Center for Mathematical Economics Working Papers, no.636, Bielefeld: Center for Mathematical Economics.
E. Bandini, et al., Optimal Dividend Payout under Stochastic Discounting, Center for Mathematical Economics Working Papers, vol. 636, Bielefeld: Center for Mathematical Economics, 2020.
Bandini, E., de Angelis, T., Ferrari, G., Gozzi, F.: Optimal Dividend Payout under Stochastic Discounting. Center for Mathematical Economics Working Papers, 636. Center for Mathematical Economics, Bielefeld (2020).
Bandini, Elena, de Angelis, Tiziano, Ferrari, Giorgio, and Gozzi, Fausto. Optimal Dividend Payout under Stochastic Discounting. Bielefeld: Center for Mathematical Economics, 2020. Center for Mathematical Economics Working Papers. 636.
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