线性约束下保险公司的最优投资策略

现实中,保险公司的投资行为会受到《保险法》及其自身风险管理条例的约束; 另外,保险公司必须提存一定数量的准备金以满足监管规定.鉴于此,本文将保险公司盈余首达最低准备金水平的时刻定义为``破产”时刻,以最小化``破产”概率为目标, 假设保险公司的盈余过程服从扩散模型,其可投资无风险资产与一种风险资产且投资受线性约束.我们通过求解相应的HJB方程得到了值函数与最优投资策略的解析式并给出了经济解释与数值算例.

Optimal Investment Strategy for Insurers under Linear Constraint

In practice, investment behaviors of an insurer will be subjected to some constraints from Insurance Law and the insurer's own risk management. Additionally, an insurer should draw certain reserve to satisfy regulatory requirements. Therefore, in this paper we suppose the time when its surplus first comes up to the floor level of reserve as the ``ruin' time; the target of the insurance company is to minimize the ``ruin' probability; the surplus process of the insurer is derived by a diffusion model and its investment behaviors are subjected to a linear constraint. By solving the corresponding HJB equation, the optimal investment strategy and value function are derived explicitly when the insurer is allowed to investment on a risk-free asset and a risky asset. In the end, economic analysis and numerical examples are provided.