An Optimal Dividend Problem with Capital Injections over a Finite Horizon

Ferrari G, Schuhmann P (2018) Center for Mathematical Economics Working Papers; 595.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
optimal dividend problem; capital injections; singular stochastic control; optimal stopping; free boundary
Erscheinungsjahr
2018
Band
595
Seite(n)
30
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2930440

Zitieren

Ferrari G, Schuhmann P. An Optimal Dividend Problem with Capital Injections over a Finite Horizon . Center for Mathematical Economics Working Papers. Vol 595. Bielefeld: Center for Mathematical Economics; 2018.
Ferrari, G., & Schuhmann, P. (2018). An Optimal Dividend Problem with Capital Injections over a Finite Horizon (Center for Mathematical Economics Working Papers, 595). Bielefeld: Center for Mathematical Economics.
Ferrari, G., and Schuhmann, P. (2018). An Optimal Dividend Problem with Capital Injections over a Finite Horizon . Center for Mathematical Economics Working Papers, 595, Bielefeld: Center for Mathematical Economics.
Ferrari, G., & Schuhmann, P., 2018. An Optimal Dividend Problem with Capital Injections over a Finite Horizon , Center for Mathematical Economics Working Papers, no.595, Bielefeld: Center for Mathematical Economics.
G. Ferrari and P. Schuhmann, An Optimal Dividend Problem with Capital Injections over a Finite Horizon , Center for Mathematical Economics Working Papers, vol. 595, Bielefeld: Center for Mathematical Economics, 2018.
Ferrari, G., Schuhmann, P.: An Optimal Dividend Problem with Capital Injections over a Finite Horizon . Center for Mathematical Economics Working Papers, 595. Center for Mathematical Economics, Bielefeld (2018).
Ferrari, Giorgio, and Schuhmann, Patrick. An Optimal Dividend Problem with Capital Injections over a Finite Horizon . Bielefeld: Center for Mathematical Economics, 2018. Center for Mathematical Economics Working Papers. 595.
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2019-09-06T09:19:01Z
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