IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2511.03031.html

Robust optimal consumption, investment and reinsurance for recursive preferences

Author

Listed:
  • Elizabeth Dadzie
  • Wilfried Kuissi-Kamdem
  • Marcel Ndengo

Abstract

This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer's surplus follows the diffusion approximation of the Cram\'er-Lundberg model, and the insurer can purchase proportional reinsurance. Model ambiguity is characterised by a class of equivalent probability measures, and the insurer, being ambiguity-averse, aims to maximise utility under the worst-case scenario. By solving the associated coupled forward-backward stochastic differential equation (FBSDE), we derive closed-form solutions for the optimal strategies and the value function. Our analysis reveals how ambiguity aversion, risk aversion, and the elasticity of intertemporal substitution (EIS) influence the optimal policies. Numerical experiments illustrate the effects of key parameters, showing that optimal consumption decreases with higher risk aversion and EIS, while investment and reinsurance strategies are co-dependent on both financial and insurance market parameters, even without correlation. This study provides a comprehensive framework for insurers to manage capital allocation and risk transfer under deep uncertainty.

Suggested Citation

  • Elizabeth Dadzie & Wilfried Kuissi-Kamdem & Marcel Ndengo, 2025. "Robust optimal consumption, investment and reinsurance for recursive preferences," Papers 2511.03031, arXiv.org.
    • Handle: RePEc:arx:papers:2511.03031
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2511.03031
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Qiang Zhang & Ping Chen, 2020. "Optimal Reinsurance and Investment Strategy for an Insurer in a Model with Delay and Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 777-801, June.
    2. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    4. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    5. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    6. Jingtang Ma & Zhengyang Lu & Dengsheng Chen, 2023. "Optimal reinsurance-investment with loss aversion under rough Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 23(1), pages 95-109, January.
    7. Chen, Zhiping & Yang, Peng, 2020. "Robust optimal reinsurance–investment strategy with price jumps and correlated claims," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 27-46.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    2. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    3. Guan, Guohui & Hu, Jiaqi & Liang, Zongxia, 2022. "Robust equilibrium strategies in a defined benefit pension plan game," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 193-217.
    4. Maenhout, Pascal J. & Vedolin, Andrea & Xing, Hao, 2025. "Robustness and dynamic sentiment," Journal of Financial Economics, Elsevier, vol. 163(C).
    5. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    6. Stan Olijslagers & Sweder Wijnbergen, 2024. "Discounting the Future: On Climate Change, Ambiguity Aversion and Epstein–Zin Preferences," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 87(3), pages 683-730, March.
    7. Nina Boyarchenko & Mario Cerrato & John Crosby & Stewart Hodges, 2012. "No good deals—no bad models," Staff Reports 589, Federal Reserve Bank of New York.
    8. Jang, Bong-Gyu & Lee, Seungkyu & Lim, Byung Hwa, 2016. "Robust consumption and portfolio rules with time-varying model confidence," Finance Research Letters, Elsevier, vol. 18(C), pages 342-352.
    9. Meyer-Gohde, Alexander, 2019. "Generalized entropy and model uncertainty," Journal of Economic Theory, Elsevier, vol. 183(C), pages 312-343.
    10. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    11. Wahid Faidi & Anis Matoussi & Mohamed Mnif, 2017. "Optimal Stochastic Control Problem Under Model Uncertainty With Nonentropy Penalty," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-41, May.
    12. Philipp Karl ILLEDITSCH, 2009. "Ambiguous Information, Risk Aversion, and Asset Pricing," 2009 Meeting Papers 802, Society for Economic Dynamics.
    13. Vedolin, Andrea & Maenhout, Pascal & Xing, Hao, 2020. "Generalized Robustness and Dynamic Pessimism," CEPR Discussion Papers 14592, C.E.P.R. Discussion Papers.
    14. Daniele Pennesi, 2013. "Asset Prices in an Ambiguous Economy," Carlo Alberto Notebooks 315, Collegio Carlo Alberto.
    15. So, Leh-chyan, 2013. "Are Real Options “Real”? Isolating Uncertainty from Risk in Real Options Analysis," MPRA Paper 52493, University Library of Munich, Germany.
    16. Balter, Anne G. & Pelsser, Antoon, 2020. "Pricing and hedging in incomplete markets with model uncertainty," European Journal of Operational Research, Elsevier, vol. 282(3), pages 911-925.
    17. Pascal J. Maenhout & Andrea Vedolin & Hao Xing, 2020. "Generalized Robustness and Dynamic Pessimism," NBER Working Papers 26970, National Bureau of Economic Research, Inc.
    18. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    19. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    20. Souza, Thiago de Oliveira, 2020. "Dollar carry timing," Discussion Papers on Economics 10/2020, University of Southern Denmark, Department of Economics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2511.03031. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.