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Optimal Deterministic Investment Strategies for Insurers

Author

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  • Nicole Bäuerle

    (Department of Mathematics, Karlsruhe Institute of Technology, Karlsruhe D-76128, Germany)

  • Ulrich Rieder

    (Department of Optimization and Operations Research, University of Ulm, Ulm D-89069, Germany)

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.

Suggested Citation

  • Nicole Bäuerle & Ulrich Rieder, 2013. "Optimal Deterministic Investment Strategies for Insurers," Risks, MDPI, vol. 1(3), pages 1-18, November.
    • Handle: RePEc:gam:jrisks:v:1:y:2013:i:3:p:101-118:d:30247
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    References listed on IDEAS

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    1. Pablo Antolin & Stéphanie Payet & Juan Yermo, 2010. "Assessing Default Investment Strategies in Defined Contribution Pension Plans," OECD Journal: Financial Market Trends, OECD Publishing, vol. 2010(1), pages 87-115.
    2. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    3. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    4. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    5. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    6. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    7. Nicole Bäuerle, 2005. "Benchmark and mean-variance problems for insurers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 159-165, September.
    8. Wenjing Guo & Chengming Xu, 2004. "Optimal portfolio selection when stock prices follow an jump-diffusion process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 485-496, December.
    9. Chamberlain, Gary, 1983. "A characterization of the distributions that imply mean--Variance utility functions," Journal of Economic Theory, Elsevier, vol. 29(1), pages 185-201, February.
    10. Łukasz Delong & Russell Gerrard, 2007. "Mean-variance portfolio selection for a non-life insurance company," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 339-367, October.
    11. Bäuerle, Nicole & Blatter, Anja, 2011. "Optimal control and dependence modeling of insurance portfolios with Lévy dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 398-405, May.
    12. Nicole Bauerle & Erhan Bayraktar, 2012. "A Note on Applications of Stochastic Ordering to Control Problems in Insurance and Finance," Papers 1210.3800, arXiv.org, revised Jul 2013.
    13. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
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    Cited by:

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    2. Falkowski, Adrian & Słomiński, Leszek, 2021. "Mean reflected stochastic differential equations with two constraints," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 172-196.

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