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

Thesis (doctoral)--Universität Hamburg.

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

(no abstract available)

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 stop-loss reinsurance is first shown to be an optimal contract under law-invariant 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 stop-loss reinsurances, insurance layers serve as the optimal solution in these cases. These two results hint that law-invariant 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 stop-loss reinsurances are shown to minimize a general law-invariant convex risk measure of the total retained risk. Sufficient condition for ordering the optimal deductibles are also obtained. Next, a Principal-Agent 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 tailor-made 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 first-best 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) quota-share 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 stop-loss form under both classes (i) and (ii); while on the other hand, its non-stop-loss nature under class (iii) is revealed. Lastly, a class of nonzero-sum 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 regime-switching Cramer-Lundberg approximation. It is a diffusion risk process with coefficients being modulated by both a continuous-time finite-state 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

In this thesis I study the nature of decision making under uncertainty in the case of natural catastrophes and reinsurance underwriting at Lloyd's of London. I begin by describing the broad context of natural catastrophes and society, which forms the basis for a market in catastrophe reinsurance. I then proceed to a review of literatures in risk, uncertainty, philosophy, and probability as a prelude to an analysis of decision making under catastrophic risk. According to the early 20th century philosopher-economist Frank Knight, risk specified those cases in which a frequency probability could be assigned, while situations of uncertainty do not allow a frequency probability since they are unique instances. In the thesis, I make the additional argument that risk and uncertainty are not solely categories of probability, but rather categories of probability and causality. The second main strand of the thesis refers to J.M. Keynes' work on probability which while related to frequency probability, is different in its emphasis on judgment and the assessment of information. I propose a causal framework to Keynes' weight of argument approach in terms of J.L. Mackie's causal field. With these two main ideas on probability and the addition of the causal field, the thesis presents the theoretical basis of its model of decision making. The last component of the model is developed through a review and critique of the economic literature on decision making under uncertainty. As the literature is founded upon frequency probability definitions of risk, the thesis argues through its theoretical investigations that this approach neglects the causal element of decision making, and that uncertainty requires a broader conceptualization than simply lack of probability. This final component, decision making routines, combines both individual and organizational elements. The empirical investigation of catastrophe risk underwriting at Lloyd's is organized into categories of decision making within a situated market context. I investigate the dominant categories and find that capital capacity and relationships drive reinsurance praxis. As an integration of its theoretical and empirical components, the thesis applies its risk decision making model. This model has implications for economic geography studies of the firm, in that it provides an epistemic and organizational basis for the formalization of tacit knowledge. The model also holds consequences for economic decision making theory, in that it integrates causal assessment in the purely probability based economic paradigm.

Thesis (M. Phil.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 106-116) Also available in print.

Thesis (Ph. D.)--Catholic University of America, 1921. / Imprint from p. [4] cover. A study of the "Military and Naval Insurance Act of October 6, 1917, an amendment to the War Risk Insurance Act of September 2, 1914."--P. 7-8. Reproduction of original from Connecticut State Library. Bibliography: p. 87.

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

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