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Optimal consumption, investment and insurance with insurable risk for an investor in a Lévy market

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  • Perera, Ryle S.

Abstract

Numerous researchers have applied the martingale approach for models driven by Lévy processes to study optimal investment problems. The aim of this paper is to apply the martingale approach to obtain a closed form solution for the optimal investment, consumption and insurance strategies of an individual in the presence of an insurable risk when the insurable risk and risky asset returns are described by Lévy processes and the utility is a constant absolute risk aversion (CARA). The model developed in this paper can potentially be applied to absorb large insurable losses in the absence of insurance protection and to examine the level of diminishing current utility and consumption.

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  • Perera, Ryle S., 2010. "Optimal consumption, investment and insurance with insurable risk for an investor in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 479-484, June.
    • Handle: RePEc:eee:insuma:v:46:y:2010:i:3:p:479-484
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    References listed on IDEAS

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    1. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
    2. Moore, Kristen S. & Young, Virginia R., 2006. "Optimal insurance in a continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 47-68, August.
    3. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Zhou, Qing, 2009. "Optimal investment for an insurer in the Lévy market: The martingale approach," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1602-1607, July.
    5. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
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    Cited by:

    1. Ryle S. Perera & Kimitoshi Sato, 2018. "Optimal asset allocation for a bank under risk control," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-27, September.
    2. Zou, Bin & Cadenillas, Abel, 2014. "Explicit solutions of optimal consumption, investment and insurance problems with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 159-167.
    3. Weiwei Shen & Juliang Yin, 2022. "Optimal Investment and Risk Control Strategies for an Insurer Subject to a Stochastic Economic Factor in a Lévy Market," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2913-2931, December.
    4. Zou, Bin & Cadenillas, Abel, 2014. "Optimal investment and risk control policies for an insurer: Expected utility maximization," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 57-67.
    5. Ryle Perera, 2013. "Optimal investment, consumption–leisure, insurance and retirement choice," Annals of Finance, Springer, vol. 9(4), pages 689-723, November.
    6. Li, Wenyuan & Tan, Ken Seng & Wei, Pengyu, 2021. "Demand for non-life insurance under habit formation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 38-54.
    7. Peng, Xingchun & Wang, Wenyuan, 2016. "Optimal investment and risk control for an insurer under inside information," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 104-116.
    8. Zhou, Jieming & Yang, Xiangqun & Guo, Junyi, 2017. "Portfolio selection and risk control for an insurer in the Lévy market under mean–variance criterion," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 139-149.
    9. Ramírez, Hugo E. & Serrano, Rafael, 2025. "Optimal investment with insurable background risk and nonlinear portfolio allocation frictions," Applied Mathematics and Computation, Elsevier, vol. 485(C).
    10. Bin Zou & Abel Cadenillas, 2014. "Optimal Investment and Risk Control Problem for an Insurer: Expected Utility Maximization," Papers 1402.3560, arXiv.org, revised Mar 2014.
    11. Jin Sun & Ryle S. Perera & Pavel V. Shevchenko, 2019. "Optimal Investment-Consumption-Insurance with Durable and Perishable Consumption Goods in a Jump Diffusion Market," Papers 1903.00631, arXiv.org.
    12. Bin Zou & Abel Cadenillas, 2014. "Explicit Solutions of Optimal Consumption, Investment and Insurance Problem with Regime Switching," Papers 1402.3562, arXiv.org, revised Jun 2014.

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