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Portfolio and reinsurance optimization under unknown market price of risk

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  • Claudia Ceci
  • Katia Colaneri

Abstract

We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving different filtrations, into an equivalent stochastic control problem under the observation filtration only, the so-called separated problem. The Markovian structure of the separated problem allows us to apply a classical approach to stochastic optimization based on the Hamilton-Jacobi-Bellman equation, and to provide explicit formulas for the value function and the optimal investment-reinsurance strategy. We finally discuss some comparisons between the optimal strategies pursued by a partially informed insurer and that followed by a fully informed insurer, and we evaluate the value of information using the idea of indifference pricing. These results are also supported by numerical experiments.

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  • Claudia Ceci & Katia Colaneri, 2024. "Portfolio and reinsurance optimization under unknown market price of risk," Papers 2408.07432, arXiv.org.
    • Handle: RePEc:arx:papers:2408.07432
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    References listed on IDEAS

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    1. Nicole Bäuerle & Gregor Leimcke, 2021. "Robust optimal investment and reinsurance problems with learning," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(2), pages 82-109, February.
    2. Li, Yongwu & Qiao, Han & Wang, Shouyang & Zhang, Ling, 2015. "Time-consistent investment strategy under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 187-197.
    3. Peng, Xingchun & Hu, Yijun, 2013. "Optimal proportional reinsurance and investment under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 416-428.
    4. Sangmin Lee & Andrew Papanicolaou, 2016. "Pairs Trading Of Two Assets With Uncertainty In Co-Integration'S Level Of Mean Reversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-36, December.
    5. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2022. "Optimal reinsurance and investment under common shock dependence between financial and actuarial markets," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 252-278.
    6. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
    7. Irgens, Christian & Paulsen, Jostein, 2004. "Optimal control of risk exposure, reinsurance and investments for insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 21-51, August.
    8. Junna Bi & Jun Cai & Yan Zeng, 2021. "Equilibrium reinsurance-investment strategies with partial information and common shock dependence," Annals of Operations Research, Springer, vol. 307(1), pages 1-24, December.
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