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 |
|---|---|
| URN: | urn:nbn:de:hbz:832-epub4-22511 |
| DOI: | https://doi.org/10.1007/s13385-019-00221-1 |
| ISSN: | 2190-9733 |
| ISSN: | 2190-9741 |
| Parent Title (English): | European Actuarial Journal |
| Publisher: | Springer Berlin Heidelberg |
| Document Type: | Article |
| Language: | English |
| 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 |
| Volume: | 10 |
| Issue: | 1 |
| 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 |
| DeepGreen: | DeepGreen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |