Brinker, Leonie Violetta 
ORCID: 0000-0003-2725-1494
(2021).
Minimal Expected Time in Drawdown through Investment for an Insurance Diffusion Model.
Risks, 9 (1).
BASEL:
MDPI.
ISSN 2227-9091
Abstract
Consider an insurance company whose surplus is modelled by an arithmetic Brownian motion of not necessarily positive drift. Additionally, the insurer has the possibility to invest in a stock modelled by a geometric Brownian motion independent of the surplus. Our key variable is the (absolute) drawdown Delta of the surplus X, defined as the distance to its running maximum X over bar . Large, long-lasting drawdowns are unfavourable for the insurance company. We consider the stochastic optimisation problem of minimising the expected time that the drawdown is larger than a positive critical value (weighted by a discounting factor) under investment. A fixed-point argument is used to show that the value function is the unique solution to the Hamilton-Jacobi-Bellman equation related to the problem. It turns out that the optimal investment strategy is given by a piecewise monotone and continuously differentiable function of the current drawdown. Several numerical examples illustrate our findings.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-567468 | ||||||||
| DOI: | 10.3390/risks9010017 | ||||||||
| Journal or Publication Title: | Risks | ||||||||
| Volume: | 9 | ||||||||
| Number: | 1 | ||||||||
| Date: | 2021 | ||||||||
| Publisher: | MDPI | ||||||||
| Place of Publication: | BASEL | ||||||||
| ISSN: | 2227-9091 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/56746 |
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