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Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization

Author

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  • Claudia Ceci
  • Katia Colaneri
  • Alessandra Cretarola
Abstract
In this paper we investigate the local risk-minimization approach for a combined financial-insurance model where there are restrictions on the information available to the insurance company. In particular we assume that, at any time, the insurance company may observe the number of deaths from a specific portfolio of insured individuals but not the mortality hazard rate. We consider a financial market driven by a general semimartingale and we aim to hedge unit-linked life insurance contracts via the local risk-minimization approach under partial information. The F\"ollmer-Schweizer decomposition of the insurance claim and explicit formulas for the optimal strategy for pure endowment and term insurance contracts are provided in terms of the projection of the survival process on the information flow. Moreover, in a Markovian framework, we reduce to solve a filtering problem with point process observations.

Suggested Citation

  • Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2014. "Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization," Papers 1406.6902, arXiv.org.
    • Handle: RePEc:arx:papers:1406.6902
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    References listed on IDEAS

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    1. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2013. "Local risk-minimization under restricted information to asset prices," Papers 1312.4385, arXiv.org, revised Nov 2014.
    2. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.
    3. Francesca Biagini & Alessandra Cretarola & Eckhard Platen, 2012. "Local Risk-Minimization under the Benchmark Approach," Papers 1210.2337, arXiv.org.
    4. Rüdiger Frey & Thorsten Schmidt, 2012. "Pricing and hedging of credit derivatives via the innovations approach to nonlinear filtering," Finance and Stochastics, Springer, vol. 16(1), pages 105-133, January.
    5. Ceci, Claudia & Cretarola, Alessandra & Russo, Francesco, 2014. "BSDEs under partial information and financial applications," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2628-2653.
    6. Martin Schweizer, 1994. "Risk‐Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342, October.
    7. Claudia Ceci & Anna Gerardi, 2006. "A Model For High Frequency Data Under Partial Information: A Filtering Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 555-576.
    8. Riesner, Martin, 2006. "Hedging life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 599-608, June.
    9. Choulli, Tahir & Vandaele, Nele & Vanmaele, Michèle, 2010. "The Föllmer-Schweizer decomposition: Comparison and description," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 853-872, June.
    10. Vandaele, Nele & Vanmaele, Michèle, 2008. "A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1128-1137, June.
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    Citations

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    Cited by:

    1. Song, In Jung & Park, Heejung & Park, Narang & Heo, Wookjae, 2019. "The effect of experiencing a death on life insurance ownership," Journal of Behavioral and Experimental Finance, Elsevier, vol. 22(C), pages 170-176.
    2. Xie, Lin & Chen, Lv & Qian, Linyi & Li, Danping & Yang, Zhixin, 2023. "Optimal investment and consumption strategies for pooled annuity with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 129-155.
    3. Alessandra Cretarola & Benedetta Salterini, 2023. "Utility-based indifference pricing of pure endowments in a Markov-modulated market model," Papers 2301.13575, arXiv.org.
    4. Colaneri, Katia & Frey, Rüdiger, 2021. "Classical solutions of the backward PIDE for Markov modulated marked point processes and applications to CAT bonds," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 498-507.
    5. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2018. "Indifference pricing of pure endowments via BSDEs under partial information," Papers 1804.00223, arXiv.org, revised Jul 2020.
    6. Da Fonseca, José, 2024. "Pricing guaranteed annuity options in a linear-rational Wishart mortality model," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 122-131.
    7. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2017. "Unit-linked life insurance policies: Optimal hedging in partially observable market models," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 149-163.
    8. Lin, Jyh-Horng & Li, Xuelian & Lin, Panpan, 2022. "Could we rely on credit swap hedging as a substitute for insurer blockchain technology involvement?," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 266-281.

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    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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