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Optimal Insurance Strategies: A Hybrid Deep Learning Markov Chain Approximation Approach

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  • Cheng, Xiang
  • Jin, Zhuo
  • Yang, Hailiang

Abstract

This paper studies deep learning approaches to find optimal reinsurance and dividend strategies for insurance companies. Due to the randomness of the financial ruin time to terminate the control processes, a Markov chain approximation-based iterative deep learning algorithm is developed to study this type of infinite-horizon optimal control problems. The optimal controls are approximated as deep neural networks in both cases of regular and singular types of dividend strategies. The framework of Markov chain approximation plays a key role in building the iterative equations and initialization of the algorithm. We implement our method to classic dividend and reinsurance problems and compare the learning results with existing analytical solutions. The feasibility of our method for complicated problems has been demonstrated by applying to an optimal dividend, reinsurance and investment problem under a high-dimensional diffusive model with jumps and regime switching.

Suggested Citation

  • Cheng, Xiang & Jin, Zhuo & Yang, Hailiang, 2020. "Optimal Insurance Strategies: A Hybrid Deep Learning Markov Chain Approximation Approach," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 449-477, May.
    • Handle: RePEc:cup:astinb:v:50:y:2020:i:2:p:449-477_5
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    Cited by:

    1. Wenyuan Wang & Xiang Yu & Xiaowen Zhou, 2021. "On optimality of barrier dividend control under endogenous regime switching with application to Chapter 11 bankruptcy," Papers 2108.01800, arXiv.org, revised Nov 2023.
    2. Aleksandar Arandjelovi'c & Julia Eisenberg, 2024. "Reinsurance with neural networks," Papers 2408.06168, arXiv.org.
    3. Jin, Zhuo & Yang, Hailiang & Yin, G., 2021. "A hybrid deep learning method for optimal insurance strategies: Algorithms and convergence analysis," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 262-275.
    4. Qiu, Ming & Jin, Zhuo & Li, Shuanming, 2023. "Optimal risk sharing and dividend strategies under default contagion: A semi-analytical approach," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 1-23.
    5. Qiqi Wang & Katja Hanewald & Xiaojun Wang, 2022. "Multistate health transition modeling using neural networks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(2), pages 475-504, June.

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