This thesis considers one of the classical problems in the actuarial mathematics literature, the decay of the probability of ruin in the collective risk model. The
claim number process N(t) is assumed to be a renewal process, the resulting model
being referred as the Sparre Andersen risk model. The inter-claim...
In this dissertation, we study two risk models. First, we consider the dual risk process which models the surplus of a company that incurs expenses at a constant rate and earns random positive gains at random times. When the surplus is invested in a risky asset following a geometric Brownian...
An insurance company, having an initial capital u, receives premiums continuously and pays claims of random sizes at random times. A classical result states that if the rate of premium, c, exceeds the average of the claims paid per unit time, ⋋μ, then the ruin probability decays exponentially fast as...
We consider a renewal jump diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin...
Accumulation of excessive salt in irrigated soils can reduce crop yields, reduce the effectiveness of irrigation, ruin soil structure, and affect other soil properties. This publication is designed to help you evaluate the kind and amount of salts present in soils and to select management alternatives. This publication describes the...
Agricultural revenues, the product of stochastic prices and yields, lead to markets which are
incomplete, thereby entreating and complicating economic inquiry. The following three essays
explore the incomplete nature of agricultural markets and consider the implications of
incompleteness for a range of policy questions and economic tools.
The first essay,...
We introduce a model for the surplus of nonprofit organizations (NPO). We assume two types of spending schemes for an NPO. Type I is a constant spending rate and Type II is a variable rate above and below a cut-off reserve level. Under steady state, we compute and compare the...
Risk is a crucial decision factor besides traditional cost and performance during collaborative decision making in a distributed environment. Three main challenges exist: 1) stakeholders' different perspectives and/or diverse cultures can lead to inconsistent risk probability evaluations; 2) risk consequence is hard to be quantified in concrete unit; 3) risk...
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can lead to inconsistent risk probability evaluations; 2)
risk consequence is hard to be quantified
The main focus was on developing an algorithm and supporting computer programs for use by extension personel to counsel farm managers on problems of enterprise choice. Investigation was initiated from the complete certainty viewpoint of linear programming. Upon introducing uncertainty, ramifications of changing expected income, variance and the correlation coefficient...
In agriculture there has been a long history of using a levy or an insurance premium to create mutual funds to mediate economic risks to growers due to environmental variability and quarantine pests. In the United States the federal government, through the USDA, continues to underwrite funds (collected by private...