摘要
研究了具有两个业务部门的保险公司的最优投资问题,其中每个业务部门的盈余过程由二维的Lévy过程描述。保险公司可将其盈余投资于金融市场,其中金融市场由一个无风险资产和两个具有风险相关性的风险资产组成,而且风险资产的价格过程由二维的Lévy过程所驱动。文中讨论了两个优化问题。一个是基准问题,即选择适当的投资策略使保险公司的终端财富与一个基准值之差的平方期望最小;另一个是均值-方差(M-V)问题,即在保险公司终端财富给定的情形下,选择适当的投资策略使终端财富的方差最小。利用动态规划的方法,得到第一个优化问题的最优投资策略和最优值函数的解析式。结合第一个优化问题的结果,利用对偶定理得到第二个优化问题的最优投资策略和有效前沿。
Two optimal investment problems for an insurer with two business lines are considered, where each business line~ risk process is modeled by two-dimensional Lrvy process. It is assumed that the in- surer can invest its surplus in a risk-free asset and two risky assets, where the risky assets＇price processes are described by a two-dimensional Lrvy process. A benchmark problem and a mean-variance problem are discussed. The first problem is to choose the optimal investment strategy to minimize the expected quadratic distance of the risk reserve to a given benchmark; the second problem is to minimize the vari- ance of the terminal wealth when the expected terminal reserve is given. By employing stochastic dynamic programming approach, the explicit expressions of the optimal investment strategy and the optimal value function are derived for the first problem ; with the results of the first problem and the duality theory, theoptimal investment strategy and the efficient frontier for the second problem are derived.
出处
《中山大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第5期57-63,67,共8页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
国家自然科学基金资助项目(71201173
71231008)
珠江学者支持计划资助项目
广东省高层次人才资助项目
