The evaluation of risk is often performed assuming static conditions when in reality, conditions are continually evolving. In the following dissertation, the evaluation of risk with changing conditions over time is considered for a specific project - placing overburden into an active, open pit mine. The research focuses on the geotechnical components of risk with the goal of identifying whether and to what extent it is possible to place overburden on mined out portions of the open pit slopes. The relevant factors, which change with time or impact risk, are first identified and an evaluation is performed to estimate a probability of failure at various stages of the project life. Potential damages are then assessed by first evaluating the run out distance and post failure geometry of a slope failure and then estimating the percentage of material that would have to be removed to continue extraction of ore. To convert the uncertainty into economic terms, unit values for savings that result from placing overburden in the pit and costs associated with cleaning up failure debris are estimated. The probability of failure, potential for cleanup, and unit values are combined to produce estimates of the likely costs and benefits associated with dumping overburden in the open pit.The results of the analysis indicated that risk varies considerably with time. However, it is possible to place overburden in the central portion of the open pit up to a limit of approximately 80 million tons while maintaining a positive net value of expected costs and benefits.

In this thesis, we consider a risk model which incorporates multiple threshold levels characterizing an insurer's minimal capital requirement, dividend paying situations, and external financial activities. Our model is based on discrete monetary and time units, and the main quantities of interest are the finite-time ruin probabilities and the expected total discounted dividends paid prior to ruin. We mainly focus on the development of computational methods to attain these quantities of interest. One of the popular methods in the current literature used for studying such problems involves a recursive approach which incorporates appropriate conditioning arguments on the claim times and sizes, and we implement this procedure as well. Furthermore, ruin can occur due to both a claim as well as interest expense accumulation as our model allows the insurer to borrow money from an external fund. In this thesis, we consider only non-stochastic interest rates for both lending and borrowing activities. After constructing appropriate recursive formulae for the finite-time ruin probabilities and the expected total discounted dividends paid prior to ruin, we investigate various numerical examples and make some observations concerning the impact our threshold levels have on finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.

The inverse Gaussian distribution is investigated as a basis for statistical analyses of skewed and possibly censored response times. This distribution arises from a random walk process, is a member of the exponential family, and admits the sample arithmetic and harmonic means as complete sufficient statistics. In addition, the inverse Gaussian provides a reasonable alternative to the more commonly used lognormal statistical model due to the attractive properties of its parameter estimates. / Three modifications were made to the basic distribution definition: adding a shift parameter to account for minimum latencies, allowing for Type I censoring, and convoluting two inverse Gaussian random variables in order to model components of response times. Corresponding parameter estimation and large sample test procedures were also developed. / Results from analysing two extensive sets of simple and two-choice reaction times suggest that shifting the origin and accounting for Type I censoring can substantially improve the reliability of inverse Gaussian parameter estimates. The results also indicate that the convolution model provides a convenient medium for probing underlying psychological processes.

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The probabilistic method in combinatorics is a nonconstructive tool popularized through the work of Paul Erd˝os. Many difficult problems can be solved through a relatively simple application of probability theory that can lead to solutions which are better than known constructive methods. This thesis presents some of the basic tools used throughout the probabilistic method along with some of the applications of the probabilistic method throughout the fields of Ramsey theory, graph theory and other areas of combinatorial analysis. Then the topic of random graphs is covered. The theory of random graphs was founded during the late fifties and early sixties to study questions involving the effect of probability distributions upon graphical properties. This thesis presents some of the basic results involving graph models and graph properties.

No description available.

No description available.

The probabilistic method in combinatorics is a nonconstructive tool popularized through the work of Paul Erd˝os. Many difficult problems can be solved through a relatively simple application of probability theory that can lead to solutions which are better than known constructive methods. This thesis presents some of the basic tools used throughout the probabilistic method along with some of the applications of the probabilistic method throughout the fields of Ramsey theory, graph theory and other areas of combinatorial analysis. Then the topic of random graphs is covered. The theory of random graphs was founded during the late fifties and early sixties to study questions involving the effect of probability distributions upon graphical properties. This thesis presents some of the basic results involving graph models and graph properties.

No description available.