Titelaufnahme

Titel
An optimal dividend problem with capital injections over a finite horizon / Giorgio Ferrari and Patrick Schuhmann
VerfasserFerrari, Giorgio In der Gemeinsamen Normdatei der DNB nachschlagen ; Schuhmann, Patrick
ErschienenBielefeld : Center for Mathematical Economics (IMW), April 2018
Ausgabe
Elektronische Ressource
Umfang1 Online-Ressource (29 Seiten)
SerieCenter for Mathematical Economics Working papers ; 595
URNurn:nbn:de:hbz:6:2-103416 Persistent Identifier (URN)
Zugriffsbeschränkung
 Das Dokument ist frei verfügbar.
Dateien
An optimal dividend problem with capital injections over a finite horizon [0.44 mb]
Zusammenfassung

In this paper we propose and solve an optimal dividend problem with capital injections over a finite time horizon. The surplus dynamics obeys a linearly controlled drifted Brownian motion that is reflected at zero, dividends give rise to time-dependent instantaneous marginal profits, whereas capital injections are subject to time-dependent instantaneous marginal costs. The aim is to maximize the sum of a liquidation value at terminal time and of the total expected profits from dividends, net of the total expected costs for capital injections. Inspired by the study in [13] on reflected follower problems, we relate the optimal dividend problem with capital injections to an optimal stopping problem for a drifted Brownian motion that is absorbed at zero. We show that whenever the optimal stopping rule is triggered by a time-dependent boundary, the value function of the optimal stopping problem gives the derivative of the value function of the optimal dividend problem. Moreover, the optimal dividends' distribution strategy is also triggered by the moving boundary of the associated stopping problem. The properties of this boundary are then investigated in a case study in which instantaneous marginal profits and costs from dividends and capital injections are constants discounted at a constant rate.

Klassifikation
Links
Nachweis