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Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option

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  • Zhongyang Sun
  • Xin Zhang
  • Kam Chuen Yuen

Abstract

This paper considers an optimal asset-liability management (ALM) problem for an insurer under the mean-variance criterion. It is assumed that the value of liabilities is described by a geometric Brownian motion (GBM). The insurer's surplus process is modeled by a general jump process generated by a marked point process. The financial market consists of one risk-free asset and n risky assets with the risk premium relying on an affine diffusion factor process. By transferring a proportion of insurance risk to a reinsurer and investing the surplus into the financial market, the insurer aims to maximize the expected terminal net wealth and, at the same time, minimize the corresponding variance of the terminal net wealth. By using a backward stochastic differential equation (BSDE) approach, closed-form expressions for both the efficient strategy and efficient frontier are derived. To illustrate the main results, we study an example with the Heston stochastic volatility (SV) model and numerically analyze the economic behavior of the efficient frontier. Finally, a generalization of the Mutual Fund Theorem is obtained.

Suggested Citation

  • Zhongyang Sun & Xin Zhang & Kam Chuen Yuen, 2020. "Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(3), pages 218-244, March.
    • Handle: RePEc:taf:sactxx:v:2020:y:2020:i:3:p:218-244
    DOI: 10.1080/03461238.2019.1658619
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    Cited by:

    1. Yumo Zhang, 2023. "Robust Optimal Investment Strategies for Mean-Variance Asset-Liability Management Under 4/2 Stochastic Volatility Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-32, March.
    2. Wang, Ning & Zhang, Yumo, 2023. "Robust optimal asset-liability management with mispricing and stochastic factor market dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 251-273.

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