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基于新巴塞尔协议监管下保险人的均值-方差最优投资-再保险问题
Optimal Mean-Variance Investment-Reinsurance Problem with Constrained Controls by the New Basel Regulations for an Insurer
本文研究了均值-方差优化准则下，保险人的最优投资和最优再保险问题.我们用一个复合泊松过程模型来拟合保险人的风险过程，保险人可以投资无风险资产和价格服从跳跃-扩散过程的风险资产.此外保险人还可以购买新的业务（如再保险）.本文的限制条件为投资和再保险策略均非负，即不允许卖空风险资产，且再保险的比例系数非负.除此之外，本文还引入了新巴塞尔协议对风险资产进行监管，使用随机二次线性（linear-quadratic，LQ）控制理论推导出最优值和最优策略.对应的哈密顿-雅克比-贝尔曼（Hamilton-Jacobi-Bellman，HJB）方程不再有古典解.在粘性解的框架下，我们给出了新的验证定理，并得到有效策略（最优投资策略和最优再保险策略）的显式解和有效前沿.
We study the optimal investment and optimal reinsurance problem for an insurer under the criterion of mean-variance. The insurer's risk process is modeled by a compound Poisson process and the insurer can invest in a risk-free asset and a risky asset whose price follows a jump-diffusion process. In addition, the insurer can purchase new business (such as reinsurance). The controls (investment and reinsurance strategies) are constrained to take nonnegative values due to nonnegative new business and no-shorting constraint of the risky asset. We control the risk by the new Basel regulation and use the stochastic linear-quadratic (LQ) control theory to derive the optimal value and the optimal strategy. The corresponding Hamilton-Jacobi-Bellman (HJB) equation no longer has a classical solution. With the framework of viscosity solution, we give a new verification theorem, and then the efficient strategy (optimal investment strategy and optimal reinsurance strategy) and the efficient frontier are derived explicitly.
均值-方差准则 / 最优投资-再保险 / 新巴塞尔协议 / HJB方程 / 验证定理 {{custom_keyword}} /
mean-variance portfolio selection / optimal investment reinsurance / new Basel regulation / HJB equation / verification theorem {{custom_keyword}} /
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国家自然科学基金资助项目（11571189，11871219，11871220，11901201）；111引智计划（B14019）
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