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Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option
Scandinavian Actuarial Journal ( IF 1.8 ) Pub Date : 2019-08-31 , DOI: 10.1080/03461238.2019.1658619
Zhongyang Sun 1 , Xin Zhang 2 , Kam Chuen Yuen 3
Affiliation  

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.

中文翻译:

具有仿射扩散因子过程和再保险选项的均值方差资产负债管理

摘要 本文考虑了在均值方差准则下保险公司的最优资产负债管理 (ALM) 问题。假设负债的价值由几何布朗运动 (GBM) 描述。保险公司的盈余过程由标记点过程生成的一般跳跃过程建模。金融市场由一种无风险资产和 n 种风险资产组成,风险溢价依赖于仿射扩散因子过程。通过将一定比例的保险风险转移给再保险公司,将盈余投资于金融市场,保险公司的目标是最大化预期终端净财富,同时最小化终端净财富的相应方差。通过使用后向随机微分方程 (BSDE) 方法,推导出有效策略和有效边界的闭式表达式。为了说明主要结果,我们用 Heston 随机波动率 (SV) 模型研究了一个例子,并对有效前沿的经济行为进行了数值分析。最后,得到共同基金定理的推广。
更新日期:2019-08-31
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