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1 
Robustness of generalized estimating equations in credibility modelsHuang, Danwei., 黃丹薇. January 2007 (has links)
published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

2 
Optimal reinsurance: a contemporary perspectiveSung, Kachun, Joseph., 宋家俊. January 2012 (has links)
In recent years, general risk measures have played an important role in risk management
in both finance and insurance industry. As a consequence, there is an
increasing number of research on optimal reinsurance problems using risk measures
as yard sticks beyond the classical expected utility framework.
In this thesis, the stoploss reinsurance is first shown to be an optimal contract
under lawinvariant convex risk measures via a new simple geometric argument.
This similar approach is then used to tackle the same optimal reinsurance problem
under Value at Risk and Conditional Tail Expectation; it is interesting to note
that, instead of stoploss reinsurances, insurance layers serve as the optimal solution
in these cases. These two results hint that lawinvariant convex risk measure
may be better and more robust to expected larger claims than Value at Risk and
Conditional Tail Expectation even though they are more commonly used.
In addition, the problem of optimal reinsurance design for a basket of n insurable
risks is studied. Without assuming any particular dependence structure, a
minimax optimal reinsurance decision formulation for the problem has been successfully
proposed. To solve it, the least favorable dependence structure is first
identified, and then the stoploss reinsurances are shown to minimize a general
lawinvariant convex risk measure of the total retained risk. Sufficient condition
for ordering the optimal deductibles are also obtained.
Next, a PrincipalAgent model is adopted to describe a monopolistic reinsurance
market with adverse selection. Under the asymmetry of information, the reinsurer
(the principal) aims to maximize the average profit by selling a tailormade reinsurance
to every insurer (agent) from a (huge) family with hidden characteristics.
In regard to Basel Capital Accord, each insurer uses Value at Risk as the risk assessment,
and also takes the right to choose different risk tolerances. By utilizing
the special features of insurance layers, their optimality as the firstbest strategy
over all feasible reinsurances is proved. Also, the same optimal reinsurance
screening problem is studied under other subclass of reinsurances: (i) deductible
contracts; (ii) quotashare reinsurances; and (iii) reinsurance contracts with convex
indemnity, with the aid of indirect utility functions. In particular, the optimal
indirect utility function is shown to be of the stoploss form under both classes
(i) and (ii); while on the other hand, its nonstoploss nature under class (iii) is
revealed.
Lastly, a class of nonzerosum stochastic differential reinsurance games between
two insurance companies is studied. Each insurance company is assumed to maximize
the difference of the opponent’s terminal surplus from that of its own by
properly arranging its reinsurance schedule. The surplus process of each insurance
company is modeled by a mixed regimeswitching CramerLundberg approximation.
It is a diffusion risk process with coefficients being modulated by both
a continuoustime finitestate Markov Chain and another diffusion process; and
correlations among these surplus processes are allowed. In contrast to the traditional
HJB approach, BSDE method is used and an explicit Nash equilibrium is
derived. / published_or_final_version / Mathematics / Master / Master of Philosophy

3 
A framework for the regulation of longterm insurers : solvency assessment and the role of the statutory actuaryViljoen, Dirk Johannes 18 September 2012 (has links)
In this dissertation the theory of solvency assessment for longterm insurers is reviewed and how it evolved. Key international bodies and standards are identified and selected jurisdictions’ solvency frameworks are reviewed. The South African framework required by legislation introduced in 1998 is compared to these standards. Solvency capital requirements, valuation methods and risk management standards are the key areas considered. The financial results of a model office according to the South African requirements are compared to the financial results modelled stochastically according to the identified international standards.
It is shown that the South African framework does not meet international standards. The key problem areas are the prescribed nature of the solvency capital requirement, the onerous treatment of policy cancellations and the treatment of new business.
The role of actuaries in solvency assessment is also investigated. South Africa’s statutoryactuary role is compared with similar international roles. It is concluded that although similar international roles, notably the appointed actuary of the UK, have evolved the role of the statutory actuary has remained the same.

4 
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

5 
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

6 
Ruin theory under uncertain investmentsConstantinescu, Corina D. 11 June 2003 (has links)
Graduation date: 2004

7 
Makehamizing mortality data by least squares curve fittingRuth, Oscar E. January 1978 (has links)
This thesis explores the feasibility of the application of statistical regression theory to the curve fitting of mortality data. Equations derived from Makeham's first law were used. These include:1x = ksxgcXlog lx=a+hx+bcx color pX = A + BcxThe 1941 CSO and 1958 CSO mortality tables were used for initial study.Extending this work, pure raw mortality data in conjunction with a modified version of the last equation above was employed. Results were quite interesting.

8 
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

9 
Some results on BSDEs with applications in finance and insuranceLin, Yin, 林印 January 2013 (has links)
Considerably much work has been done on Backward Stochastic Differential Equations (BSDEs) in continuoustime with deterministic terminal horizon or stopping times. Various new models have been introduced in these years in order to generalize BSDEs to solve new practical financial problems.
One strand is focused on discretetime models. Backward Stochastic Difference Equations (also called BSDEs if no ambiguity) on discretetime finitestate space were introduced by Cohen and Elliott (2010a). The associated theory required only weak assumptions. In the first topic of this thesis, properties of nonlinear expectations defined using the discretetime finitestate BSDEs were studied. A converse comparison theorem was established. Properties of risk measures defined by nonlinear expectations, especially the representation theorems, were given. Then the theory of BSDEs was applied to optimal design of dynamic risk measures. Another strand is about a general random terminal time, which is not necessarily a stopping time. The motivation of this model is a financial problem of hedging of defaultable contingent claims, where BSDEs with stopping times are not applicable. In the second topic of this thesis, discretetime finitestate BSDEs under progressively enlarged filtration were considered. Martingale representation
theorem, existence and uniqueness theorem and comparison theorem were established. Application to nonlinear expectations was also explored. Using the theory of BSDEs, the explicit solution for optimal design of dynamic default risk measures was obtained.
In recent work on continuoustime BSDEs under progressively enlarged filtration, the reference filtration is generated by Brownian motions. In order to deal with cases with jumps, in the third topic of this thesis, a general reference filtration with predictable representation property and an initial time with immersion property were considered. The martingale representation theorem for squareintegrable martingales under progressively enlarged filtration was established. Then the existence and uniqueness theorem of BSDEs under enlarged filtration using Lipschitz continuity of the driver was proved. Conditions for a comparison theorem were also presented. Finally applications to nonlinear expectations and hedging of defaultable contingent claims on BrownianPoisson setting were explored. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

10 
Ruin analysis of correlated aggregate claims modelsWan, Laimei. January 2005 (has links)
published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

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