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Optimal Capital Injections and Dividends with Tax in a Risk Model in Discrete Time

  • We consider a risk model in discrete time with dividends and capital injections. The goal is to maximise the value of a dividend strategy. We show that the optimal strategy is of barrier type. That is, all capital above a certain threshold is paid as dividend. A second problem adds tax to the dividends but an injection leads to an exemption from tax. We show that the value function fulfils a Bellman equation. As a special case, we consider the case of premia of size one. In this case we show that the optimal strategy is a two barrier strategy. That is, there is a barrier if a next dividend of size one can be paid without tax and a barrier if the next dividend of size one will be taxed. In both models, we illustrate the findings by de Finetti’s example.

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Author:Katharina Bata, Hanspeter Schmidli
Parent Title (English):European Actuarial Journal
Publisher:Springer Berlin Heidelberg
Document Type:Article
Date of first Publication:2020/06/01
Date of Publication (online):2023/06/19
GND-Keyword:Bellman-Gleichung; Steuer
Tag:60J10; 60K30; Bellman Equation; Capital Injections; Discrete Risk Model; Optimal Dividend Problem; Primary 91B30; Secondary 60G42; Tax; Two Barrier Strategy; de Finetti Model
Page Number:25
Institutes:Anlagen, Energie- und Maschinensysteme (F09) / Fakultät 09 / Institut für Produktentwicklung und Konstruktionstechnik
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften
Open Access:Open Access
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International