Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option
Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option
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DOI：
10.1080/03461238.2019.1658619
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发表时间：
2020-03
影响因子：
1.8
通讯作者：
Zhongyang Sun;Xin Zhang;K. Yuen
中科院分区：
文献类型：
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作者：
Zhongyang Sun;Xin Zhang;K. Yuen
摘要本文研究了均值-方差准则下保险公司的最优资产负债管理问题。假设负债的价值由几何布朗运动（GBM）描述。保险人的盈余过程是由一个标记点过程产生的一般跳过程来模拟的。金融市场由一个无风险资产和n个风险资产组成，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人，并将盈余投资于金融市场，保险人的目标是最大化预期的终端净财富，同时最小化相应的终端净财富的方差。通过使用向后随机微分方程（BERO）的方法，封闭形式的有效策略和有效边界的表达式。为了说明主要结果，我们研究了一个例子与赫斯顿随机波动率（SV）模型和数值分析的有效前沿的经济行为。最后，得到了共同基金定理的一个推广。
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.