Other Statistics and Probability Commons^™

Addressing The Impact Of Time-Dependent Social Groupings On Animal Survival And Recapture Rates In Mark-Recapture Studies, Alexandru M. Draghici

Electronic Thesis and Dissertation Repository

Mark-recapture (MR) models typically assume that individuals under study have independent survival and recapture outcomes. One such model of interest is known as the Cormack-Jolly-Seber (CJS) model. In this dissertation, we conduct three major research projects focused on studying the impact of violating the independence assumption in MR models along with presenting extensions which relax the independence assumption. In the first project, we conduct a simulation study to address the impact of failing to account for pair-bonded animals having correlated recapture and survival fates on the CJS model. We examined the impact of correlation on the likelihood ratio test (LRT), …

Testing Aftershock Forecasts Using Bayesian Methods, Elisa Dong

Electronic Thesis and Dissertation Repository

The presence of strong aftershocks can increase the seismic hazard following a large earthquake and should be considered for operational earthquake forecasting and risk management. Aftershock forecasts are generated from seismicity models during the evolution of the aftershock sequence. This work compares quantitative test results of the forecasting abilities for three competing aftershock rate models - the modified Omori law, the Epidemic Type Aftershock Sequence model, and the compound Omori law - to identify the best performing model for forecasting the largest aftershock during the early aftershock sequence. Forecasts of large aftershock probabilities are generated by either the Extreme Value …

On The Sparre-Andersen Risk Models, Ruixi Zhang

Electronic Thesis and Dissertation Repository

This thesis develops several strategies for calculating ruin-related quantities for a variety of extended risk models. We focus on the Sparre-Andersen risk model, also known as the renewal risk model. The idea of arbitrary distribution for the waiting time between claim payments arose in the 1950’s from the collective risk theory, and received many extensions and modifications in recent years. Our goal is to tackle model assumptions that are either too relaxed for traditional methods to apply, or so complicated that elaborate algebraic tools are needed to obtain explicit solutions.

In Chapter 2, we consider a Lévy risk process and …

Some Recent Developments On Pareto-Optimal Reinsurance, Wenjun Jiang

Electronic Thesis and Dissertation Repository

This thesis focuses on developing Pareto-optimal reinsurance policy which considers the interests of both the insurer and the reinsurer. The optimal insurance/reinsurance design has been extensively studied in actuarial science literature, while in early years most studies were concentrated on optimizing the insurer’s interests. However, as early as 1960s, Borch argued that “an agreement which is quite attractive to one party may not be acceptable to its counterparty” and he pioneered the study on “fair” risk sharing between the insurer and the reinsurer. Quite recently, the question of how to strike a balance in risk sharing between an insurer and …

Valuation And Risk Management Of Some Longevity And P&C Insurance Products, Yixing Zhao

Electronic Thesis and Dissertation Repository

Numerous insurance products linked to risky assets have emerged rapidly in the last couple of decades. These products have option-embedded features and typically involve at least two risk factors, namely interest and mortality risks. The need for models to capture risk factors' behaviours accurately is enormous and critical for insurance companies. The primary objective of this thesis is to develop pricing and hedging frameworks for option-embedded longevity products addressing correlated risk factors. Various methods are employed to facilitate the computation of prices and risk measures of longevity products including those with maturity benefits. Furthermore, in order to be prepared for …

Advances In Semi-Nonparametric Density Estimation And Shrinkage Regression, Hossein Zareamoghaddam

Electronic Thesis and Dissertation Repository

This thesis advocates the use of shrinkage and penalty techniques for estimating the parameters of a regression model that comprises both parametric and nonparametric components and develops semi-nonparametric density estimation methodologies that are applicable in a regression context.

First, a moment-based approach whereby a univariate or bivariate density function is approximated by means of a suitable initial density function that is adjusted by a linear combination of orthogonal polynomials is introduced. Such adjustments are shown to be mathematically equivalent to making use of standard polynomials in one or two variables. Once extended to apply to density estimation, in which case …

Completely Monotone And Bernstein Functions With Convexity Properties On Their Measures, Shen Shan

Electronic Thesis and Dissertation Repository

The concepts of completely monotone and Bernstein functions have been introduced near one hundred years ago. They find wide applications in areas ranging from stochastic L\'{e}vy processes and complex analysis to monotone operator theory. They have well-known Bernstein and L\'{e}vy-Khintchine integral representations through which there are one-to-one correspondences between them and Radon measures on $[0,\infty)$ or $(0,\infty)$, respectively. In this thesis, we investigate subclasses of completely monotone and Bernstein functions with various convexity properties on their measures. These subclasses have intriguing applications in probability theories and convex analysis.

The convexity properties we investigate include convexity, harmonic convexity and $\beta$-convexity of …

On The Dual Risk Models, Chen Yang

Electronic Thesis and Dissertation Repository

Abstract This thesis focuses on developing and computing ruin-related quantities that are potentially measurements for the dual risk models which was proposed to describe the annuity-type businesses from the perspective of the collective risk theory in 1950’s. In recent years, the dual risk models are revisited by many researchers to quantify the risk of the similar businesses as the annuity-type businesses. The major extensions included in this thesis consist of two aspects: the first is to search for new ruin-related quantities that are potentially indices of the risk for well-established dual models; the other aspect is to generalize the settings …

Perfect And Nearly Perfect Sampling Of Work-Conserving Queues, Yaofei Xiong

Electronic Thesis and Dissertation Repository

We present sampling-based methods to treat work-conserving queueing systems. A variety of models are studied. Besides the First Come First Served (FCFS) queues, many efforts are putted on the accumulating priority queue (APQ), where a customer accumulates priority linearly while waiting. APQs have Poisson arrivals, multi-class customers with corresponding service durations, and single or multiple servers.

Perfect sampling is an approach to draw a sample directly from the steady-state distribution of a Markov chain without explicitly solving for it. Statistical inference can be conducted without initialization bias. If an error can be tolerated within some limit, i.e. the total variation …

Risk Models With Dependence And Perturbation, Zhong Li

Electronic Thesis and Dissertation Repository

In ruin theory, the surplus process of an insurance company is usually modeled by the classical compound Poisson risk model or its general version, the Sparre-Andersen risk model. Under these models, the claim amounts and the inter-claim times are assumed to be independently distributed, which is not always appropriate in practice. In recent years, risk models relaxing the independence assumption have drawn increasing attention. However, previous research mostly considers the so call dependent Sparre-Andersen risk model under which the pairs of random variables consisting of the inter-claim time and the next claim amount remain independent of each other. In this …

Valuation And Risk Measurement Of Guaranteed Annuity Options Under Stochastic Environment, Huan Gao

Electronic Thesis and Dissertation Repository

This thesis develops stochastic modelling frameworks for the accurate pricing and risk management of complex insurance products with option-embedded features. We propose stochastic models for the evolution of the two main risk factors, the interest rate and mortality rate, which could also have a correlation structure. For the valuation problem, a general framework is put forward where correlated interest and mortality rates are modelled as affine-diffusion processes. A new concept of endowment-risk-adjusted measure is introduced to facilitate the calculation of the GAO value. As a natural offshoot of addressing GAO valuation, we derive the convex-order upper and lower bounds of …

Stochastic Simulation And Spatial Statistics Of Large Datasets Using Parallel Computing, Jonathan Sw Lee

Electronic Thesis and Dissertation Repository

Lattice models are a way of representing spatial locations in a grid where each cell is in a certain state and evolves according to transition rules and rates dependent on a surrounding neighbourhood. These models are capable of describing many phenomena such as the simulation and growth of a forest fire front. These spatial simulation models as well as spatial descriptive statistics such as Ripley's K-function have wide applicability in spatial statistics but in general do not scale well for large datasets. Parallel computing (high performance computing) is one solution that can provide limited scalability to these applications. This is …

Comparison Of Option Pricing Between Arma-Garch And Garch-M Models, Yi Xi

Electronic Thesis and Dissertation Repository

Option pricing is a major area in financial modeling. Option pricing is sometimes based on normal GARCH models. Normal GARCH models fail to capture the skewness and the leptokurtosis in financial data. The variant GARCH-in-mean (GARCH-M) model is widely used in the option pricing literature. It adds a heteroskedasticity term to the mean equation, which is interpreted as a risk premium, and also incorporates a type of asymmetry.

Our goal is to compare option valuation between GARCH-M and ARMA-GARCH models with normal and non-normal, z-distributed innovations. The models are fitted to the historical return data, and risk neutral measures are …

The Construction Of Edmond Halley's 1701 Map Of Magnetic Declination, Lori L. Murray

Electronic Thesis and Dissertation Repository

Using the navigational instruments of his time, Edmond Halley collected data during sea voyages of the HMS Paramore. Following these voyages, in 1701 he published a map showing lines of equal magnetic declination. Magnetic declination or variation is the angular difference between magnetic north and geographical or true north for any point on the earth’s surface. The map has been held up by many as an early, and good, example of statistical graphics. Halley did not reveal the data analytic techniques that he used in his map construction and they remain unknown to this day. Using some mathematical tools of …

Advances In Graph-Cut Optimization: Multi-Surface Models, Label Costs, And Hierarchical Costs, Andrew T. Delong

Electronic Thesis and Dissertation Repository

Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or energy minimization. This is particularly true of "low-level" inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy would, hypothetically, yield a good solution to the corresponding problem. Unfortunately, even for low-level problems we are confronted by energies that are computationally hard—often NP-hard—to minimize. As a consequence, a rather large portion of computer vision research is dedicated to proposing …