Abstract: A SVR-based quantitative calculation method was proposed, so that the relevant theory of incentive contract could be analyzed quantitatively and be put into practical use. Being able to calculate quantitatively, the Support Vector Regression (SVR) was used to express the utility function. Based on that, the gradient expression of adverse selection model was derived for both good natural condition and bad condition, and that of adverse selection model was also derived for both high efficient Agent and low efficient Agent, respectively. Then, the relevant gradient descent algorithm was given. Using the proposed method, the two adverse selection incentive contract models above were quantitatively analyzed, and the effects of varying parameters on the changing trends of adverse selection model equilibriums were observed. The reasonable results show that it is feasible to solve adverse selection incentive contract model using the SVR-based quantitative calculation method.

Key words: Support Vector Regression (SVR), utility function, adverse selection, incentive contract

摘要： 为解决激励合约理论的量化分析和实际应用问题，提出了基于支持向量回归机(SVR)的逆向选择合约模型的数值分析方法。利用SVR对效用函数建模，解决了效用函数无法用解析函数表达的问题。在此基础上，分别推导出了自然条件好与差两种情形下逆向选择模型的梯度表达式、代理人高效率类型和低效率类型的逆向选择模型的梯度表达式，并给出了相应的梯度法迭代算法。利用这一算法进行数值计算和量化分析，观察上述两种逆向选择模型中参数变化对合约均衡点变化趋势的影响。计算结果表明用基于SVR的数值分析方法定量分析激励合约模型是可行的。

关键词: 支持向量回归机, 效用函数, 逆向选择, 激励合约