published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

In the literature of ruin theory, there have been extensive studies trying to generalize the classical insurance risk model. In this thesis, we look into two particular risk processes considering multi-dimensional risk and dependent structures respectively. The first one is a bivariate risk process with a dividend barrier, which concerns a two-dimensional risk model under a barrier strategy. Copula is used to represent the dependence between two business lines when a common shock strikes. By defining the time of ruin to be the first time that either of the two lines has its surplus level below zero, we derive a discrete approximation procedure to calculate the expected discounted dividends until ruin under such a model. A thorough discussion of application in proportional reinsurance with numerical examples is provided as well as an examination of the joint optimal dividend barrier for the bivariate process. The second risk process is a semi-Markovian dual risk process. Assuming that the dependence among innovations and waiting times is driven by a Markov chain, we analyze a quantity resembling the Gerber-Shiu expected discounted penalty function that incorporates random variables defined before and after the time of ruin, such as the minimum surplus level before ruin and the time of the first gain after ruin. General properties of the function are studied, and some exact results are derived upon distributional assumptions on either the inter-arrival times or the gain amounts. Applications in a perpetual insurance and the last inter-arrival time before ruin are given along with some numerical examples. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Traditionally, in the context of ruin theory, most judgements are made on an immediate sense. An example would be the determination of ruin, in which a business is declared broke right away when it attains a negative surplus. Another example would be the decision on dividend payment, in which a business pays dividends whenever the surplus level overshoots certain threshold. Such scheme of decision making is generally being criticized as unrealistic from a practical point of view. The Parisian concept is therefore invoked to handle this issue. This idea is deemed more realistic since it allows certain delay in the execution of decisions. In this thesis, such Parisian concept is utilized on two different aspects. The first one is to incorporate this concept on defining ruin, leading to the introduction of Parisian ruin time. Under such a setting, a business is considered ruined only when the surplus level stays negative continuously for a prescribed length of time. The case for a fixed delay is considered. Both the renewal risk model and the dual renewal risk model are studied. Under a mild distributional assumption that either the inter arrival time or the claim size is exponentially distributed (while keeping the other arbitrary), the Laplace transform to the Parisian ruin time is derived. Numerical example is performed to confirm the reasonableness of the results. The methodology in obtaining the Laplace transform to the Parisian ruin time is also demonstrated to be useful in deriving the joint distribution to the number of negative surplus causing or without causing Parisian ruin. The second contribution is to incorporate this concept on the decision for dividend payment. Specifically, a business only pays lump-sum dividends when the surplus level stays above certain threshold continuously for a prescribed length of time. The case for a fixed and an Erlang(n) delay are considered. The dual compound Poisson risk model is studied. Laplace transform to the ordinary ruin time is derived. Numerical examples are performed to illustrate the results. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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.

Wong, Shiu Fung. / "July 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 36-38). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Participating policy --- p.4 / Chapter 3 --- Levy Process and its use in financial modelling --- p.8 / Chapter 3.1 --- Levy process in asset modelling --- p.8 / Chapter 3.2 --- Levy process in derivative pricing --- p.11 / Chapter 3.2.1 --- Review of FFT methods in option pricing --- p.12 / Chapter 3.2.2 --- Expectation using FFT --- p.13 / Chapter 4 --- Network methodology --- p.17 / Chapter 4.1 --- Asset dynamic: Network Approach --- p.17 / Chapter 4.1.1 --- Transition probability by FFT --- p.18 / Chapter 4.1.2 --- Example in American option pricing --- p.19 / Chapter 4.2 --- Extended Network for Participating Contract --- p.20 / Chapter 4.3 --- Practical network construction --- p.22 / Chapter 4.3.1 --- Modified network-drift offsetting --- p.23 / Chapter 4.3.2 --- Logarithmic scale network --- p.25 / Chapter 4.4 --- Incorporating surrender rights and mortality --- p.26 / Chapter 4.4.1 --- Surrender right --- p.26 / Chapter 4.4.2 --- Mortality --- p.27 / Chapter 4.5 --- Proof of convergence --- p.28 / Chapter 5 --- Numerical Results --- p.32 / Chapter 5.1 --- The Black and Scholes model --- p.33 / Chapter 5.2 --- The Merton's Jump diffusion model --- p.33 / Chapter 5.3 --- Variance gamma model --- p.34 / Chapter 6 --- Conclusion --- p.35 / Bibliography --- p.36

Cheung, Oi Lam Eunice. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 43-45). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Risk Theory --- p.1 / Chapter 1.2 --- Hybrid Numerical Scheme --- p.3 / Chapter 2 --- The Model --- p.5 / Chapter 2.1 --- Model --- p.5 / Chapter 2.2 --- Integro-Differential Equations --- p.8 / Chapter 2.3 --- Explicit Formulas and Asymptotic Properties --- p.13 / Chapter 3 --- Numerical Method --- p.16 / Chapter 3.1 --- From Integro-Differential Equations to Integral Equations --- p.17 / Chapter 3.2 --- Prom Integral Equations to Linear Equations --- p.19 / Chapter 3.3 --- Boundary Conditions --- p.20 / Chapter 3.4 --- Importance Sampling --- p.23 / Chapter 4 --- Numerical Study --- p.27 / Chapter 4.1 --- Exponential Claims with Equal Means --- p.28 / Chapter 4.1.1 --- Importance Sampling --- p.28 / Chapter 4.1.2 --- System of Linear Equations --- p.31 / Chapter 4.2 --- Exponential Claims with Unequal Means --- p.32 / Chapter 5 --- Conclusion --- p.40 / Bibliography --- p.43

Leung, Kit Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 47-48). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Classical Model --- p.1 / Chapter 1.2 --- Diffusion-perturbed model --- p.3 / Chapter 1.3 --- Hybrid computational scheme --- p.5 / Chapter 2 --- Integro-differential Equations --- p.7 / Chapter 2.1 --- Integro-differential equation of Chiu and Yin (2003) --- p.7 / Chapter 2.2 --- Integro-differential equations for ψs(u) and ψd(u) --- p.16 / Chapter 3 --- Numerical Method --- p.17 / Chapter 3.1 --- Trapezoidal approximation --- p.18 / Chapter 3.2 --- Boundary Conditions --- p.19 / Chapter 4 --- Importance Sampling --- p.22 / Chapter 4.1 --- Simulation Recipe --- p.25 / Chapter 4.2 --- Discussion --- p.26 / Chapter 5 --- Numerical Examples --- p.28 / Chapter 5.1 --- Probabilities of ruin: Oscillation and claim --- p.28 / Chapter 5.2 --- Comparison with the asymptotic results --- p.32 / Chapter 5.2.1 --- Ruin Probability --- p.38 / Chapter 5.2.2 --- Surplus before ruin --- p.40 / Chapter 5.2.3 --- Deficit after ruin --- p.42 / Chapter 6 --- Conclusion --- p.45 / References --- p.47

Graduation date: 2004