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Optimal Deterministic Investment Strategies for Insurers
Department of Mathematics, Karlsruhe Institute of Technology, Karlsruhe D-76128, Germany
Department of Optimization and Operations Research, University of Ulm, Ulm D-89069, Germany
* Author to whom correspondence should be addressed.
Received: 30 September 2013; in revised form: 28 October 2013 / Accepted: 2 November 2013 / Published: 7 November 2013
Abstract: 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
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Bäuerle, N.; Rieder, U. Optimal Deterministic Investment Strategies for Insurers. Risks 2013, 1, 101-118.
Bäuerle N, Rieder U. Optimal Deterministic Investment Strategies for Insurers. Risks. 2013; 1(3):101-118.
Bäuerle, Nicole; Rieder, Ulrich. 2013. "Optimal Deterministic Investment Strategies for Insurers." Risks 1, no. 3: 101-118.