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

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The stability-diversity-complexity debate has persisted as a central focus of theoretical ecology for half a century. The debate concerns the deceptively simple question of whether there is a causal relationship between the complexity and/or diversity of biological communities and their stability. Historical analysis of the debate shows that conflicting claims different studies seem to support indicate an underlying lack of conceptual clarity about the three concepts. The problem of defining these concepts is thus at the debate's core, and finding adequate definitions is one objective of the dissertation. The absence of consensus about how ecological stability should be defined, for instance, reflects uncertainty about what properties of a community should be considered its stability, resulting in studies that suggest conflicting conclusions based on different senses of the concept. For this reason, some philosophers have claimed that proposed definitions of ecological stability are incompatible and that the concept is itself problematic. I argue, however, that three unproblematic concepts are jointly sufficient and individually necessary for ecological stability. Another issue concerns whether the mathematical concept of Lyapunov stability utilized in physics adequately defines ecological stability, as many theoretical ecologists assume. I argue that it does not because it cannot adequately represent perturbations against which community stability must be assessed. The project of defining these particular concepts raises a more fundamental issue: what adequacy criteria should definitions in general satisfy? Against the prevailing view that definitions must preserve meaning exactly, I argue there are good reasons to require definitions preserve only similarity of meaning with the defined concept. Following Carnap, I call such definitions 'explicative'. The prevailing view is clearly unproblematic if the definitional goal is simply to clarify the actual meaning of concepts. It is problematic, however, if the objective is to provide normative guidance about concepts. Concepts play an indispensable role in the acquisition of knowledge. As such, definitional modifications of our conceptual apparatus should be evaluated by epistemic advantages or disadvantages they procure. I argue the advantages afforded by an explicative definition --such as enhancing precision, testability, theoretical unification, etc.-- justify forgoing strong similarity with the concept being defined.

My dissertation consists of three essays that examine the role of fixed factors in multi-sector neoclassical growth models, specifically the role of population density in causing the onset of industrialization. The first paper examines the question of why industrialization occurred first in China rather than England. Although industrialization first occurred in England, it is often thought that China, not England, was the world leader in technology at the time. Yet China did not industrialize until 150 years after England and nearly a century after less advanced European countries. This puzzle is examined in a two-sector model with competing agrarian and industrial production technologies. I find that when differences in population density across countries are accounted for, this delayed industrialization by China is the result of decreasing returns to population density in the agrarian technology and is consistent with the theory. In the second paper, the importance of total factor productivity (TFP) in causing industrialization is examined. TFP has long been thought to be the driving force behind industrialization. However, such an explanation cannot adequately account for the staggered timing of industrialization across countries. By accounting for differences in population density, a heterogeneity previously unexplored in the literature, I can account for 49-51 percent of the movement toward industrialization in the two sector overlapping generations model employed by Hansen and Prescott (2002). The third paper presents a sequential competitive equilibrium to solve an infinite horizon two-sector neoclassical growth mode where the two sectors are chosen to represent the agrarian and manufacturing sectors of the economy. In this framework, industrialization is seen to be the relaxing of the non-negativity constrain on the manufacturing sector. It is seen that every country possesses a critical population density upon which it will transition from using solely an agrarian production technology to employing both agrarian and manufacturing technologies. This transition is result of a discrete change in the decision to invest in manufacturing capital. Furthermore, the ability of agents to anticipate industrialization is shown to increase the rate of capital accumulation and hasten the onset of the manufacturing sector.

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