This thesis contains three parts: an optimal insurance contract design problem under Yarri’s dual model, that under the Rank-Dependent Expected Utility (RDEU) model, and that involving two insureds with RDEU and Expected Utility (EU) preference respectively. / In the first part, we propose an optimal insurance problem in which the insured’s preference is indicated by Yaari’s preference. We consider generally nonlinear type of contracts while requiring the indemnity function be a non-decreasing function of the losses, which reduces potential moral hazard. The probability weighting (or distortion) function in our model is inverse-S shaped, which is consistent with the experimental study. We use the quantile formulation method to solve this problem completely and analytically. We also present the results when the indemnity function is not required to be non-decreasing, for the purpose of comparing with the results when the indemnity function is non-decreasing. Moreover, an alternative model under Wang’s premium principle is also studied in this part. / In the second part, we focus on an optimal insurance problem in the framework of RDEU theory. This problem has been studied in the literature; however, the existing results suffer from a severe problem of moral hazard, because the contract derived is not a non-decreasing indemnity function. In our work, we impose the requirement that indemnity function be a non-decreasing function of the loss and develop a general method to solve this problem by using the quantile formulation and calculus of variations. We also provide numerical results to demonstrate our results. / In the last part, we study an optimal insurance problem with two types of representative clients in the market. One is dictated by the classical EU preference, and the other follows the RDEU preference. The insurer is to design a menu of contracts not only to meet the needs of both types of customers but also to maximize the insurer’s own profit. We solve this problem and provide some numerical results for illustration. / 本论文包含三个部分: 在Yaari模型下的最优保险合同设计，在RDEU模型下的最优保险合同设计和一个包含RDEU和EU两类风险偏好的保险客户的最优保险合同设计。 / 在第一部分，我们提出了一个Yaari模型下的最优保险合同设计问题，也就是说在这个模型中保险客户的偏好是被Yaari型偏好来表达的。我们考虑了一般性的非线性合同，并且要求赔偿函数是一个关于损失的非递減的函数来防止潜在的道德风险。在找们的模型中，概率权重(或者是扭曲) 函数是反S型的，这一点和实验的结果是吻合的。我们利用分位数方法彻底解决了这个问题。为了对比我们的结论，我们还提供了没有限制赔偿函数必须是损失的非递减函数的结果。此外，找们还研究了在Wang的保费定价理论框架下的一个相似的保险合同设计模型。 / 在第二部分，我们研究了一个REDU模型下的最优保险合同设计问题。这个问题在保险史上被研究过。然而已有的结果会面临一个非常严重的道德风险的问题，因为最优合同不是一个关于损失的非递減函数。在找们的工作中，我们添加了赔偿函数必须是损失的非递減函数的要求，并且利用分位数形式和变分法推导了一个通常的方法解决了这个问题。并且，我们提供了一些数值结果来展示我们的结果。 / 最后一个部分，我们研究了一个在保险市场中有两类代表性客户的最优合同设计问题。其中一类的偏好是被期望效用理论表达，而另一类的偏好是被等级依赖效用理论来表达。保险公司希望设计一份保单同时满足这两类客户的需求并且使得自己的利润最大化。我们解决了这个问题并且展示了数值结果。 / Zhuang, Shengchao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 117-122). / Abstracts also in Chinese. / Title from PDF title page (viewed on 29, November, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.