多目标随机优化问题的样本均值近似及其在保险中的应用
Sample average approximation of multiobjective stochastic optimization problems with application in insurance
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中文总结 AI 辅助
本文提出用样本均值近似将多目标随机优化转化为确定性多准则问题，在向量容差内求弱帕累托有效解，并证明收敛性，应用于保险业务优化。
中文摘要 AI 辅助
本文描述了一种求解多目标随机优化问题的技术。作为待优化随机系统的广义模型，采用了一个向量（输入-随机输出）系统。随机输出被转换为确定性绩效与风险指标的向量。问题在于找到与输出指标帕累托最优值相对应的输入。该问题通过一系列确定性多准则优化问题来近似，其中，例如，目标向量函数是原始函数的样本均值近似，可行集是可行输入的离散样本近似。近似最优解被定义为在某个向量容差内的弱帕累托有效解。收敛性分析包括建立一般近似方案的收敛性，以及在适当调节采样参数下以概率1收敛的条件。所提出的技术在一个支持保险业务多准则优化的计算机系统上得到了展示。
英文摘要
The article describes a technique for solving multiobjective stochastic optimization problems. As a generalized model of a stochastic system to be optimized a vector (input-random output) system is used. Ran- dom outputs are converted into a vector of deterministic performance and risk indicators. The problem is to find those inputs that correspond to a Pareto-optimal values of output indicators. The problem is approximated by a sequence of deterministic multi-criteria optimization problems, where, for example, the objective vector function is a sample average approximation of the original one and the feasible set is a discrete sample approximation of the feasible inputs. Approximate optimal solutions are defined as weakly Pareto-efficient ones within some vector tolerance. Convergence analysis includes establishing convergence of the general approx- imation scheme and establishing conditions of convergence with probability one under proper regulation of sampling parameters. The proposed technique is illustrated on a computer system for supporting multi-criteria optimization of insurance business.
