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Risks 2013, 1(3), 101-118; doi:10.3390/risks1030101

Optimal Deterministic Investment Strategies for Insurers

1,*  and 2
1 Department of Mathematics, Karlsruhe Institute of Technology, Karlsruhe D-76128, Germany 2 Department of Optimization and Operations Research, University of Ulm, Ulm D-89069, Germany
* Author to whom correspondence should be addressed.
Received: 30 September 2013 / Revised: 28 October 2013 / Accepted: 2 November 2013 / Published: 7 November 2013
(This article belongs to the Special Issue Application of Stochastic Processes in Insurance)
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We consider an insurance company whose risk reserve is given by a Brownian motion with drift and which is able to invest the money into a Black–Scholes financial market. As optimization criteria, we treat mean-variance problems, problems with other risk measures, exponential utility and the probability of ruin. Following recent research, we assume that investment strategies have to be deterministic. This leads to deterministic control problems, which are quite easy to solve. Moreover, it turns out that there are some interesting links between the optimal investment strategies of these problems. Finally, we also show that this approach works in the Lévy process framework.
Keywords: deterministic control problem; mean-variance; risk measure; Lévy process deterministic control problem; mean-variance; risk measure; Lévy process
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bäuerle, N.; Rieder, U. Optimal Deterministic Investment Strategies for Insurers. Risks 2013, 1, 101-118.

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