保险公司在风险相依模型中均值-方差准则下的最优投资策略
发布时间：2018-08-11 10:00
【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。
[Abstract]:The optimal investment problem of insurance companies with two business units is studied, in which the earnings process of each business sector is described by a two-dimensional L 茅 vy process. Insurance companies can invest their earnings in financial markets, in which the financial market consists of a risk-free asset and two riskless risk assets, and the price process of the risky assets is driven by the two-dimensional L 茅 vy process. Two optimization problems are discussed in this paper. One is the benchmark problem, that is, choosing the appropriate investment strategy to minimize the square expectation of the difference between the terminal wealth of the insurance company and a benchmark value; the other is the mean-variance (M-V) problem, that is, when the insurance company's terminal wealth is given, Choose the appropriate investment strategy to minimize the variance of terminal wealth. The optimal investment strategy and optimal value function of the first optimization problem are obtained by using the dynamic programming method. Combined with the results of the first optimization problem, the optimal investment strategy and efficient frontier of the second optimization problem are obtained by using the duality theorem.
【作者单位】： 中山大学数学与计算科学学院;广东工业大学应用数学学院;中山大学金融工程与风险管理研究中心;
【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
【分类号】：F842.3;O212.1
[Abstract]:The optimal investment problem of insurance companies with two business units is studied, in which the earnings process of each business sector is described by a two-dimensional L 茅 vy process. Insurance companies can invest their earnings in financial markets, in which the financial market consists of a risk-free asset and two riskless risk assets, and the price process of the risky assets is driven by the two-dimensional L 茅 vy process. Two optimization problems are discussed in this paper. One is the benchmark problem, that is, choosing the appropriate investment strategy to minimize the square expectation of the difference between the terminal wealth of the insurance company and a benchmark value; the other is the mean-variance (M-V) problem, that is, when the insurance company's terminal wealth is given, Choose the appropriate investment strategy to minimize the variance of terminal wealth. The optimal investment strategy and optimal value function of the first optimization problem are obtained by using the dynamic programming method. Combined with the results of the first optimization problem, the optimal investment strategy and efficient frontier of the second optimization problem are obtained by using the duality theorem.
【作者单位】： 中山大学数学与计算科学学院;广东工业大学应用数学学院;中山大学金融工程与风险管理研究中心;
【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
【分类号】：F842.3;O212.1
【参考文献】
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1 张明善;姚s，
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