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1 
Study on insurance risk models with subexponential tails and dependence structuresChen, Yiqing, 陳宜清 January 2009 (has links)
published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

2 
Analysis of some risk processes in ruin theoryLiu, Luyin, 劉綠茵 January 2013 (has links)
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 multidimensional risk and dependent structures respectively.
The first one is a bivariate risk process with a dividend barrier, which concerns a twodimensional 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 semiMarkovian dual risk process. Assuming that the dependence among innovations and waiting times is driven by a Markov chain, we analyze a quantity resembling the GerberShiu 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 interarrival times or the gain amounts. Applications in a perpetual insurance and the last interarrival time before ruin are given along with some numerical examples. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

3 
On some Parisian problems in ruin theoryWong, Tsunyu, Jeff, 黃峻儒 January 2014 (has links)
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 lumpsum 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

4 
Ruin theory under a threshold insurance risk modelKwan, Kwokman., 關國文. January 2007 (has links)
published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

5 
Ruin theory under Markovian regimeswitching risk modelsZhu, Jinxia., 朱金霞. January 2008 (has links)
published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

6 
A numerical solution for solving ruin probability of the classical model with two classes of correlated claims.January 2008 (has links)
Cheung, Oi Lam Eunice. / Thesis (M.Phil.)Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 4345). / 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  IntegroDifferential Equations  p.8 / Chapter 2.3  Explicit Formulas and Asymptotic Properties  p.13 / Chapter 3  Numerical Method  p.16 / Chapter 3.1  From IntegroDifferential 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

7 
A hybrid method for solving the ruin functionals of the classical risk model perturbed by diffusion.January 2008 (has links)
Leung, Kit Hung. / Thesis (M.Phil.)Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 4748). / Abstracts in English and Chinese. / Chapter 1  Introduction  p.1 / Chapter 1.1  Classical Model  p.1 / Chapter 1.2  Diffusionperturbed model  p.3 / Chapter 1.3  Hybrid computational scheme  p.5 / Chapter 2  Integrodifferential Equations  p.7 / Chapter 2.1  Integrodifferential equation of Chiu and Yin (2003)  p.7 / Chapter 2.2  Integrodifferential 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

8 
Ruin theory under uncertain investmentsConstantinescu, Corina D. 11 June 2003 (has links)
Graduation date: 2004

9 
Fouriercosine method for insurance risk theoryChau, Kiwai, 周麒偉 January 2014 (has links)
In this thesis, a systematic study is carried out for effectively approximating GerberShiu functions under L´evy subordinator models. It is a hardly touched topic in the recent literature and our approach is via the popular Fouriercosine method.
In theory, classical GerberShiu functions can be expressed in terms of an infinite sum of convolutions, but its inherent complexity makes efficient computation almost impossible. In contrast, Fourier transforms of convolutions could be evaluated in a far simpler manner. Therefore, an efficient numerical method based on Fourier transform is pursued in this thesis for evaluating GerberShiu functions.
Fouriercosine method is a numerical method based on Fourier transform and has been very popular in option pricing since its introduction. It then evolves into a number of extensions, and we here adopt its spirit to insurance risk theory. In this thesis, the proposed approximant of GerberShiu functions under an L´evy subordinator model has O(n) computational complexity in comparison with that of O(n log n) via the usual numerical Fourier inversion. Also, for GerberShiu functions within the proposed refined Sobolev space, an explicit error bound is given and error bound of this type is seemingly absent in the literature.
Furthermore, the error bound for our estimation can be further enhanced under extra assumptions, which are not immediate from Fang and Oosterlee’s works. We also suggest a robust method on the estimation of ruin probabilities (one special class of GerberShiu functions) based on the moments of both claim size and claim arrival distributions. Rearrangement inequality will also be adopted to amplify the use of our Fouriercosine method in ruin probability, resulting in an effective global estimation. Finally, the effectiveness of our result will be further illustrated in a number of numerical studies and our enhanced error bound is apparently optimal in our demonstration; more precisely, empirical evidence exhibiting the biggest possible error convergence rate agrees with our theoretical conclusion. / published_or_final_version / Mathematics / Master / Master of Philosophy

10 
GerberShiu function in threshold insurance risk modelsGong, Qi, 龔綺 January 2008 (has links)
published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

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